Chargement des library

library(tidyr) #Gérer les dataframes
library(dplyr) #Gérer les dataframes
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(lubridate) #Gérer les dates
## 
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
library(FactoMineR) 
library(MASS)
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
library(cluster)
data <-read.csv("weatherAUS.csv")
head (data)
##         Date Location MinTemp MaxTemp Rainfall Evaporation Sunshine WindGustDir
## 1 2008-12-01   Albury    13.4    22.9      0.6          NA       NA           W
## 2 2008-12-02   Albury     7.4    25.1      0.0          NA       NA         WNW
## 3 2008-12-03   Albury    12.9    25.7      0.0          NA       NA         WSW
## 4 2008-12-04   Albury     9.2    28.0      0.0          NA       NA          NE
## 5 2008-12-05   Albury    17.5    32.3      1.0          NA       NA           W
## 6 2008-12-06   Albury    14.6    29.7      0.2          NA       NA         WNW
##   WindGustSpeed WindDir9am WindDir3pm WindSpeed9am WindSpeed3pm Humidity9am
## 1            44          W        WNW           20           24          71
## 2            44        NNW        WSW            4           22          44
## 3            46          W        WSW           19           26          38
## 4            24         SE          E           11            9          45
## 5            41        ENE         NW            7           20          82
## 6            56          W          W           19           24          55
##   Humidity3pm Pressure9am Pressure3pm Cloud9am Cloud3pm Temp9am Temp3pm
## 1          22      1007.7      1007.1        8       NA    16.9    21.8
## 2          25      1010.6      1007.8       NA       NA    17.2    24.3
## 3          30      1007.6      1008.7       NA        2    21.0    23.2
## 4          16      1017.6      1012.8       NA       NA    18.1    26.5
## 5          33      1010.8      1006.0        7        8    17.8    29.7
## 6          23      1009.2      1005.4       NA       NA    20.6    28.9
##   RainToday RainTomorrow
## 1        No           No
## 2        No           No
## 3        No           No
## 4        No           No
## 5        No           No
## 6        No           No
str(data)
## 'data.frame':    145460 obs. of  23 variables:
##  $ Date         : Factor w/ 3436 levels "2007-11-01","2007-11-02",..: 397 398 399 400 401 402 403 404 405 406 ...
##  $ Location     : Factor w/ 49 levels "Adelaide","Albany",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ MinTemp      : num  13.4 7.4 12.9 9.2 17.5 14.6 14.3 7.7 9.7 13.1 ...
##  $ MaxTemp      : num  22.9 25.1 25.7 28 32.3 29.7 25 26.7 31.9 30.1 ...
##  $ Rainfall     : num  0.6 0 0 0 1 0.2 0 0 0 1.4 ...
##  $ Evaporation  : num  NA NA NA NA NA NA NA NA NA NA ...
##  $ Sunshine     : num  NA NA NA NA NA NA NA NA NA NA ...
##  $ WindGustDir  : Factor w/ 16 levels "E","ENE","ESE",..: 14 15 16 5 14 15 14 14 7 14 ...
##  $ WindGustSpeed: int  44 44 46 24 41 56 50 35 80 28 ...
##  $ WindDir9am   : Factor w/ 16 levels "E","ENE","ESE",..: 14 7 14 10 2 14 13 11 10 9 ...
##  $ WindDir3pm   : Factor w/ 16 levels "E","ENE","ESE",..: 15 16 16 1 8 14 14 14 8 11 ...
##  $ WindSpeed9am : int  20 4 19 11 7 19 20 6 7 15 ...
##  $ WindSpeed3pm : int  24 22 26 9 20 24 24 17 28 11 ...
##  $ Humidity9am  : int  71 44 38 45 82 55 49 48 42 58 ...
##  $ Humidity3pm  : int  22 25 30 16 33 23 19 19 9 27 ...
##  $ Pressure9am  : num  1008 1011 1008 1018 1011 ...
##  $ Pressure3pm  : num  1007 1008 1009 1013 1006 ...
##  $ Cloud9am     : int  8 NA NA NA 7 NA 1 NA NA NA ...
##  $ Cloud3pm     : int  NA NA 2 NA 8 NA NA NA NA NA ...
##  $ Temp9am      : num  16.9 17.2 21 18.1 17.8 20.6 18.1 16.3 18.3 20.1 ...
##  $ Temp3pm      : num  21.8 24.3 23.2 26.5 29.7 28.9 24.6 25.5 30.2 28.2 ...
##  $ RainToday    : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 2 ...
##  $ RainTomorrow : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 2 1 ...
dim(data)
## [1] 145460     23

Suppression des variables inutiles : Evaporation, Sunshine, Cloud9am, Cloud3pm

Suppresion des variables liées au vent

data = data[, -c(6, 7, 8, 9, 10, 11, 12, 13, 18, 19)]
head(data)
##         Date Location MinTemp MaxTemp Rainfall Humidity9am Humidity3pm
## 1 2008-12-01   Albury    13.4    22.9      0.6          71          22
## 2 2008-12-02   Albury     7.4    25.1      0.0          44          25
## 3 2008-12-03   Albury    12.9    25.7      0.0          38          30
## 4 2008-12-04   Albury     9.2    28.0      0.0          45          16
## 5 2008-12-05   Albury    17.5    32.3      1.0          82          33
## 6 2008-12-06   Albury    14.6    29.7      0.2          55          23
##   Pressure9am Pressure3pm Temp9am Temp3pm RainToday RainTomorrow
## 1      1007.7      1007.1    16.9    21.8        No           No
## 2      1010.6      1007.8    17.2    24.3        No           No
## 3      1007.6      1008.7    21.0    23.2        No           No
## 4      1017.6      1012.8    18.1    26.5        No           No
## 5      1010.8      1006.0    17.8    29.7        No           No
## 6      1009.2      1005.4    20.6    28.9        No           No
data=data[!(rowSums(is.na(data))),] #On supprime les NA
str(data)
## 'data.frame':    124273 obs. of  13 variables:
##  $ Date        : Factor w/ 3436 levels "2007-11-01","2007-11-02",..: 397 398 399 400 401 402 403 404 405 406 ...
##  $ Location    : Factor w/ 49 levels "Adelaide","Albany",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ MinTemp     : num  13.4 7.4 12.9 9.2 17.5 14.6 14.3 7.7 9.7 13.1 ...
##  $ MaxTemp     : num  22.9 25.1 25.7 28 32.3 29.7 25 26.7 31.9 30.1 ...
##  $ Rainfall    : num  0.6 0 0 0 1 0.2 0 0 0 1.4 ...
##  $ Humidity9am : int  71 44 38 45 82 55 49 48 42 58 ...
##  $ Humidity3pm : int  22 25 30 16 33 23 19 19 9 27 ...
##  $ Pressure9am : num  1008 1011 1008 1018 1011 ...
##  $ Pressure3pm : num  1007 1008 1009 1013 1006 ...
##  $ Temp9am     : num  16.9 17.2 21 18.1 17.8 20.6 18.1 16.3 18.3 20.1 ...
##  $ Temp3pm     : num  21.8 24.3 23.2 26.5 29.7 28.9 24.6 25.5 30.2 28.2 ...
##  $ RainToday   : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 2 ...
##  $ RainTomorrow: Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 2 1 ...
attach(data)
dim(data)
## [1] 124273     13
head(data)
##         Date Location MinTemp MaxTemp Rainfall Humidity9am Humidity3pm
## 1 2008-12-01   Albury    13.4    22.9      0.6          71          22
## 2 2008-12-02   Albury     7.4    25.1      0.0          44          25
## 3 2008-12-03   Albury    12.9    25.7      0.0          38          30
## 4 2008-12-04   Albury     9.2    28.0      0.0          45          16
## 5 2008-12-05   Albury    17.5    32.3      1.0          82          33
## 6 2008-12-06   Albury    14.6    29.7      0.2          55          23
##   Pressure9am Pressure3pm Temp9am Temp3pm RainToday RainTomorrow
## 1      1007.7      1007.1    16.9    21.8        No           No
## 2      1010.6      1007.8    17.2    24.3        No           No
## 3      1007.6      1008.7    21.0    23.2        No           No
## 4      1017.6      1012.8    18.1    26.5        No           No
## 5      1010.8      1006.0    17.8    29.7        No           No
## 6      1009.2      1005.4    20.6    28.9        No           No

Ajout des variables Year, Month, Température moyenne

data <- mutate(data, Date = as.Date(Date))
data = data %>% mutate(Year = year(Date),
                       AvgTemp = (MaxTemp + MinTemp)/2)

Suppresion de la variable Date

data = data[, -1]
head(data)
##   Location MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am
## 1   Albury    13.4    22.9      0.6          71          22      1007.7
## 2   Albury     7.4    25.1      0.0          44          25      1010.6
## 3   Albury    12.9    25.7      0.0          38          30      1007.6
## 4   Albury     9.2    28.0      0.0          45          16      1017.6
## 5   Albury    17.5    32.3      1.0          82          33      1010.8
## 6   Albury    14.6    29.7      0.2          55          23      1009.2
##   Pressure3pm Temp9am Temp3pm RainToday RainTomorrow Year AvgTemp
## 1      1007.1    16.9    21.8        No           No 2008   18.15
## 2      1007.8    17.2    24.3        No           No 2008   16.25
## 3      1008.7    21.0    23.2        No           No 2008   19.30
## 4      1012.8    18.1    26.5        No           No 2008   18.60
## 5      1006.0    17.8    29.7        No           No 2008   24.90
## 6      1005.4    20.6    28.9        No           No 2008   22.15
# Group by les lignes par location et par année
by_loca <- data %>% group_by(Location, Year)
head(by_loca)
## # A tibble: 6 x 14
## # Groups:   Location, Year [1]
##   Location MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am
##   <fct>      <dbl>   <dbl>    <dbl>       <int>       <int>       <dbl>
## 1 Albury      13.4    22.9      0.6          71          22       1008.
## 2 Albury       7.4    25.1      0            44          25       1011.
## 3 Albury      12.9    25.7      0            38          30       1008.
## 4 Albury       9.2    28        0            45          16       1018.
## 5 Albury      17.5    32.3      1            82          33       1011.
## 6 Albury      14.6    29.7      0.2          55          23       1009.
## # … with 7 more variables: Pressure3pm <dbl>, Temp9am <dbl>, Temp3pm <dbl>,
## #   RainToday <fct>, RainTomorrow <fct>, Year <dbl>, AvgTemp <dbl>
# Extraire 2300 lignes pour chaque ville
by_year = by_loca %>% filter(Year >= 2010 & Year <= 2017) 
data_year<- by_year %>% group_by(Location)
data_year = data_year %>% filter(n() > 2300)
data_year <- data_year %>% slice(1:2300)

On veut étudier Sydney, Sydney est le 19e ville dans la base

On supprime la variable Location, car il n’y en a plus besoin.

dataReady = data_year[(19*2300+1):(20*2300),]
data = dataReady[, -c(1, 11, 12, 13)]
head(data)
## # A tibble: 6 x 10
##   MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am Pressure3pm
##     <dbl>   <dbl>    <dbl>       <int>       <int>       <dbl>       <dbl>
## 1    18.6    24.5      0            53          55       1022.       1020.
## 2    19.3    25.2      0            77          73       1019.       1018.
## 3    20.7    26.4      0            73          70       1017.       1015.
## 4    20.2    26.7      0            70          65       1015.       1015 
## 5    20.9    24.7      0            85          79       1018.       1017.
## 6    19.5    24.9      0.8          82          68       1019.       1018.
## # … with 3 more variables: Temp9am <dbl>, Temp3pm <dbl>, AvgTemp <dbl>
summary(data)
##     MinTemp         MaxTemp         Rainfall        Humidity9am   
##  Min.   : 9.40   Min.   :15.20   Min.   :  0.000   Min.   :40.00  
##  1st Qu.:14.60   1st Qu.:19.50   1st Qu.:  0.000   1st Qu.:62.00  
##  Median :16.70   Median :21.50   Median :  0.200   Median :70.00  
##  Mean   :16.83   Mean   :21.75   Mean   :  3.303   Mean   :71.03  
##  3rd Qu.:19.00   3rd Qu.:24.00   3rd Qu.:  1.800   3rd Qu.:80.00  
##  Max.   :23.80   Max.   :28.40   Max.   :156.800   Max.   :99.00  
##   Humidity3pm     Pressure9am      Pressure3pm        Temp9am     
##  Min.   :43.00   Min.   : 994.6   Min.   : 995.2   Min.   :12.20  
##  1st Qu.:59.00   1st Qu.:1014.2   1st Qu.:1012.5   1st Qu.:17.60  
##  Median :66.00   Median :1018.0   Median :1016.3   Median :19.60  
##  Mean   :67.94   Mean   :1017.7   Mean   :1015.9   Mean   :19.68  
##  3rd Qu.:76.00   3rd Qu.:1021.6   3rd Qu.:1019.8   3rd Qu.:21.90  
##  Max.   :98.00   Max.   :1033.0   Max.   :1030.6   Max.   :25.90  
##     Temp3pm         AvgTemp     
##  Min.   :12.30   Min.   :12.85  
##  1st Qu.:18.20   1st Qu.:17.05  
##  Median :20.20   Median :19.15  
##  Mean   :20.41   Mean   :19.29  
##  3rd Qu.:22.70   3rd Qu.:21.50  
##  Max.   :27.60   Max.   :25.95
pairs(data)

On peut par exemple dire que MinTemp, MaxTemp, Temp9am,Temp3pm sont fortement corrélées.

CAH

Les variables étant dans des unités différentes, on va travailler sur les données centrées réduites pour accorder la même importance à chaque variable et éviter que les variables à forte variance pèsent indûment sur les résultats.

data.cr <- scale(data,center=TRUE, scale=TRUE)
d.data.cr <- dist(data.cr)

On utilise la mesure de Ward :

cah.ward <- hclust(d.data.cr, method="ward.D2")

On affichage le dendrogramme :

plot(cah.ward, hang=-1, cex=0.2) 

Nombre de classes ?

Au vu du dendogramme, on va garder 4 ou 5 groupes car après les hauteurs des branches deviennent trop grandes (à l’oeil, on peut voir les paquets qui se détachent).

cah.ward$height
##    [1]   0.1720470   0.1735135   0.2019882   0.2198837   0.2601319   0.2675723
##    [7]   0.2700539   0.2721642   0.2815944   0.2847263   0.2849398   0.2856560
##   [13]   0.2869685   0.2896164   0.2975261   0.3090859   0.3124122   0.3134786
##   [19]   0.3138778   0.3247142   0.3266595   0.3284561   0.3292599   0.3333532
##   [25]   0.3350805   0.3364034   0.3368516   0.3370509   0.3440252   0.3449398
##   [31]   0.3497932   0.3498577   0.3507893   0.3519389   0.3523627   0.3524819
##   [37]   0.3528658   0.3546680   0.3547867   0.3564216   0.3576374   0.3588995
##   [43]   0.3613034   0.3623132   0.3633976   0.3633998   0.3638541   0.3650293
##   [49]   0.3654436   0.3658112   0.3682339   0.3683429   0.3695007   0.3715995
##   [55]   0.3732332   0.3732457   0.3758313   0.3767916   0.3771826   0.3800750
##   [61]   0.3802412   0.3802937   0.3823888   0.3823895   0.3828453   0.3834189
##   [67]   0.3835290   0.3845728   0.3864617   0.3868611   0.3876287   0.3880659
##   [73]   0.3890057   0.3890980   0.3895242   0.3906030   0.3919888   0.3922950
##   [79]   0.3924371   0.3947844   0.3962240   0.3967517   0.3980867   0.3989136
##   [85]   0.3991227   0.3992138   0.3993459   0.4017529   0.4022123   0.4037235
##   [91]   0.4041087   0.4045324   0.4051403   0.4051725   0.4054617   0.4067941
##   [97]   0.4072660   0.4093158   0.4099564   0.4100987   0.4103294   0.4115082
##  [103]   0.4119159   0.4135228   0.4137044   0.4148639   0.4149599   0.4155208
##  [109]   0.4160685   0.4169124   0.4171388   0.4172651   0.4180689   0.4182121
##  [115]   0.4187681   0.4188882   0.4209349   0.4219046   0.4221267   0.4243690
##  [121]   0.4259638   0.4268699   0.4269590   0.4278693   0.4279679   0.4291089
##  [127]   0.4291926   0.4292998   0.4302205   0.4319197   0.4326601   0.4334122
##  [133]   0.4337554   0.4345631   0.4350402   0.4353796   0.4356568   0.4368666
##  [139]   0.4369060   0.4370367   0.4372001   0.4377558   0.4380535   0.4382367
##  [145]   0.4397510   0.4400134   0.4404138   0.4409362   0.4439034   0.4441977
##  [151]   0.4454192   0.4459776   0.4470017   0.4471570   0.4473739   0.4474556
##  [157]   0.4475645   0.4486333   0.4490140   0.4493833   0.4494033   0.4497146
##  [163]   0.4511539   0.4512780   0.4519098   0.4528240   0.4533498   0.4540529
##  [169]   0.4547670   0.4549975   0.4551278   0.4556033   0.4566493   0.4571964
##  [175]   0.4584089   0.4587951   0.4590453   0.4598858   0.4607303   0.4608520
##  [181]   0.4614549   0.4616821   0.4622137   0.4625909   0.4637698   0.4638133
##  [187]   0.4640091   0.4649149   0.4655885   0.4659579   0.4673668   0.4677393
##  [193]   0.4690459   0.4695276   0.4698176   0.4703435   0.4713175   0.4714483
##  [199]   0.4715418   0.4719928   0.4722664   0.4724886   0.4743058   0.4749097
##  [205]   0.4750390   0.4753467   0.4755180   0.4760173   0.4763130   0.4768197
##  [211]   0.4768372   0.4775323   0.4775891   0.4783403   0.4788994   0.4792454
##  [217]   0.4799429   0.4801259   0.4802442   0.4807249   0.4808738   0.4808953
##  [223]   0.4810040   0.4810284   0.4811413   0.4825115   0.4832130   0.4835682
##  [229]   0.4836931   0.4838133   0.4840054   0.4840291   0.4846821   0.4854952
##  [235]   0.4858133   0.4858250   0.4859796   0.4861714   0.4867872   0.4868459
##  [241]   0.4870232   0.4872153   0.4872940   0.4874943   0.4878586   0.4891645
##  [247]   0.4894691   0.4906057   0.4906608   0.4907510   0.4909828   0.4912521
##  [253]   0.4913634   0.4918643   0.4939948   0.4942741   0.4948892   0.4956883
##  [259]   0.4958620   0.4963805   0.4963946   0.4966565   0.4968340   0.4972595
##  [265]   0.4986964   0.4992471   0.4994401   0.4995992   0.4999551   0.5003051
##  [271]   0.5011469   0.5014866   0.5015534   0.5020146   0.5022051   0.5024299
##  [277]   0.5036959   0.5037361   0.5039559   0.5043724   0.5049153   0.5050556
##  [283]   0.5050735   0.5057275   0.5061740   0.5072629   0.5078331   0.5081942
##  [289]   0.5088786   0.5089670   0.5089825   0.5092293   0.5096174   0.5104516
##  [295]   0.5104831   0.5105525   0.5108850   0.5117565   0.5137750   0.5138853
##  [301]   0.5139168   0.5150949   0.5159271   0.5161933   0.5166669   0.5169594
##  [307]   0.5177760   0.5177777   0.5197240   0.5209010   0.5219691   0.5230798
##  [313]   0.5235443   0.5242876   0.5245316   0.5249533   0.5250793   0.5256978
##  [319]   0.5267764   0.5281637   0.5287403   0.5291585   0.5292573   0.5299924
##  [325]   0.5302307   0.5303293   0.5304301   0.5305454   0.5307147   0.5314701
##  [331]   0.5316984   0.5319412   0.5325205   0.5333473   0.5340037   0.5342073
##  [337]   0.5350581   0.5352681   0.5352742   0.5353913   0.5357974   0.5359789
##  [343]   0.5364216   0.5375554   0.5378575   0.5381178   0.5382075   0.5388712
##  [349]   0.5396812   0.5400154   0.5405008   0.5415133   0.5420501   0.5423900
##  [355]   0.5437357   0.5437366   0.5443979   0.5445930   0.5450730   0.5458465
##  [361]   0.5462779   0.5472794   0.5478320   0.5480793   0.5496510   0.5499766
##  [367]   0.5502935   0.5504866   0.5505006   0.5505111   0.5512156   0.5517601
##  [373]   0.5520516   0.5527569   0.5541879   0.5551790   0.5556946   0.5566856
##  [379]   0.5582908   0.5592755   0.5596421   0.5603415   0.5606536   0.5607627
##  [385]   0.5616991   0.5619940   0.5626323   0.5628597   0.5631373   0.5632752
##  [391]   0.5633626   0.5637562   0.5639557   0.5641037   0.5641073   0.5642562
##  [397]   0.5646278   0.5648792   0.5649092   0.5655445   0.5657308   0.5661559
##  [403]   0.5663763   0.5669713   0.5670314   0.5670817   0.5675395   0.5677002
##  [409]   0.5679579   0.5682146   0.5690487   0.5694279   0.5704550   0.5707574
##  [415]   0.5711662   0.5728152   0.5729869   0.5735997   0.5740152   0.5749858
##  [421]   0.5757448   0.5763547   0.5763754   0.5764903   0.5766049   0.5766483
##  [427]   0.5778814   0.5781381   0.5783530   0.5790533   0.5790576   0.5795935
##  [433]   0.5800595   0.5804845   0.5805716   0.5809323   0.5813397   0.5814221
##  [439]   0.5820453   0.5822978   0.5823265   0.5824230   0.5830428   0.5834003
##  [445]   0.5834422   0.5839208   0.5852485   0.5856622   0.5864159   0.5869482
##  [451]   0.5875058   0.5883280   0.5888936   0.5890567   0.5898794   0.5900479
##  [457]   0.5900811   0.5904486   0.5912619   0.5925459   0.5925503   0.5926218
##  [463]   0.5928408   0.5929967   0.5930578   0.5931589   0.5942565   0.5943622
##  [469]   0.5946798   0.5947566   0.5955459   0.5958344   0.5970810   0.5978248
##  [475]   0.5979488   0.5980189   0.5986285   0.5987837   0.5989970   0.5991942
##  [481]   0.5996818   0.6012273   0.6026977   0.6028101   0.6036655   0.6037686
##  [487]   0.6037793   0.6043971   0.6057045   0.6059844   0.6068265   0.6069370
##  [493]   0.6071993   0.6072429   0.6078185   0.6078396   0.6082642   0.6084317
##  [499]   0.6084709   0.6093026   0.6100874   0.6101582   0.6101912   0.6120671
##  [505]   0.6123505   0.6135468   0.6136606   0.6144772   0.6149056   0.6149129
##  [511]   0.6150027   0.6152683   0.6156887   0.6158643   0.6162696   0.6163508
##  [517]   0.6170226   0.6171641   0.6178025   0.6181326   0.6182480   0.6191734
##  [523]   0.6196822   0.6203448   0.6204031   0.6208267   0.6218585   0.6219552
##  [529]   0.6219964   0.6220917   0.6221632   0.6222702   0.6222736   0.6230694
##  [535]   0.6231105   0.6234716   0.6238224   0.6240087   0.6255160   0.6260563
##  [541]   0.6267204   0.6268092   0.6271448   0.6272539   0.6277706   0.6279162
##  [547]   0.6282287   0.6283807   0.6288149   0.6288543   0.6290747   0.6290813
##  [553]   0.6290851   0.6292470   0.6294951   0.6295094   0.6297444   0.6301531
##  [559]   0.6310636   0.6311600   0.6319232   0.6321069   0.6321139   0.6323634
##  [565]   0.6324723   0.6330740   0.6332367   0.6337600   0.6347275   0.6348634
##  [571]   0.6359859   0.6363688   0.6365959   0.6369307   0.6371972   0.6373597
##  [577]   0.6375979   0.6383095   0.6395948   0.6396201   0.6398157   0.6399707
##  [583]   0.6407148   0.6407494   0.6414107   0.6414145   0.6417679   0.6464921
##  [589]   0.6468493   0.6473786   0.6499946   0.6500850   0.6522767   0.6524527
##  [595]   0.6530745   0.6532812   0.6539397   0.6547936   0.6550731   0.6557741
##  [601]   0.6558859   0.6561392   0.6563774   0.6564890   0.6566702   0.6569562
##  [607]   0.6570556   0.6571304   0.6571731   0.6574828   0.6576909   0.6578396
##  [613]   0.6582966   0.6589668   0.6590079   0.6592026   0.6592760   0.6594312
##  [619]   0.6598085   0.6598643   0.6600175   0.6601224   0.6605549   0.6607632
##  [625]   0.6607775   0.6614931   0.6622284   0.6623421   0.6625877   0.6630426
##  [631]   0.6634070   0.6636007   0.6638680   0.6645037   0.6645683   0.6646792
##  [637]   0.6647822   0.6649450   0.6653527   0.6657818   0.6665917   0.6666693
##  [643]   0.6666694   0.6670533   0.6672472   0.6676359   0.6683242   0.6684060
##  [649]   0.6685801   0.6698160   0.6703558   0.6707486   0.6712143   0.6714618
##  [655]   0.6715783   0.6722902   0.6724245   0.6729780   0.6731359   0.6732837
##  [661]   0.6733428   0.6736430   0.6737178   0.6739161   0.6739849   0.6743818
##  [667]   0.6744256   0.6745169   0.6752646   0.6760485   0.6761329   0.6762121
##  [673]   0.6765666   0.6767281   0.6773006   0.6776340   0.6778213   0.6781997
##  [679]   0.6784096   0.6787985   0.6789063   0.6790873   0.6804800   0.6805075
##  [685]   0.6806905   0.6828364   0.6829118   0.6831741   0.6847412   0.6852247
##  [691]   0.6874662   0.6878623   0.6882655   0.6889137   0.6889517   0.6893856
##  [697]   0.6897498   0.6898005   0.6903260   0.6910015   0.6913858   0.6914827
##  [703]   0.6924833   0.6926349   0.6932108   0.6940506   0.6941197   0.6943662
##  [709]   0.6944098   0.6945250   0.6947297   0.6953701   0.6954768   0.6956493
##  [715]   0.6957698   0.6964421   0.6977119   0.6996477   0.7007595   0.7013184
##  [721]   0.7014812   0.7028200   0.7029957   0.7035111   0.7037445   0.7039246
##  [727]   0.7040444   0.7043317   0.7047833   0.7054661   0.7055949   0.7056347
##  [733]   0.7068715   0.7073508   0.7074637   0.7077110   0.7087836   0.7098421
##  [739]   0.7101903   0.7111526   0.7114827   0.7124953   0.7131578   0.7135208
##  [745]   0.7136413   0.7136564   0.7147591   0.7157803   0.7159525   0.7163795
##  [751]   0.7164814   0.7165156   0.7166195   0.7167620   0.7171236   0.7176044
##  [757]   0.7193216   0.7204757   0.7213360   0.7214573   0.7219203   0.7219808
##  [763]   0.7223345   0.7233101   0.7238130   0.7239552   0.7260479   0.7260554
##  [769]   0.7265269   0.7270687   0.7270819   0.7274054   0.7278557   0.7286287
##  [775]   0.7292351   0.7297960   0.7307108   0.7314116   0.7315704   0.7315967
##  [781]   0.7326208   0.7328390   0.7329917   0.7366144   0.7372214   0.7375794
##  [787]   0.7377639   0.7381805   0.7383337   0.7383556   0.7385348   0.7398265
##  [793]   0.7399820   0.7405464   0.7408120   0.7409964   0.7410111   0.7411708
##  [799]   0.7412307   0.7417766   0.7418449   0.7425892   0.7426334   0.7427022
##  [805]   0.7434729   0.7436950   0.7449410   0.7451874   0.7455157   0.7457445
##  [811]   0.7457526   0.7459263   0.7461097   0.7470316   0.7473041   0.7473187
##  [817]   0.7474035   0.7474061   0.7484093   0.7489785   0.7493281   0.7495657
##  [823]   0.7497207   0.7500929   0.7503066   0.7520410   0.7527497   0.7527899
##  [829]   0.7533940   0.7535343   0.7536037   0.7536737   0.7537319   0.7538011
##  [835]   0.7538413   0.7538870   0.7541718   0.7541800   0.7551531   0.7554594
##  [841]   0.7558550   0.7560256   0.7571993   0.7573526   0.7574973   0.7576225
##  [847]   0.7582795   0.7584277   0.7585818   0.7592316   0.7593949   0.7594891
##  [853]   0.7599164   0.7605026   0.7609557   0.7618434   0.7618756   0.7637994
##  [859]   0.7643282   0.7651233   0.7652028   0.7656360   0.7657412   0.7658847
##  [865]   0.7670805   0.7671554   0.7679937   0.7682854   0.7683725   0.7685994
##  [871]   0.7694849   0.7694940   0.7698605   0.7701457   0.7707251   0.7715425
##  [877]   0.7724837   0.7730683   0.7738784   0.7746644   0.7748349   0.7749892
##  [883]   0.7750304   0.7750390   0.7751741   0.7764139   0.7764205   0.7779722
##  [889]   0.7783211   0.7787744   0.7793399   0.7796585   0.7800115   0.7800367
##  [895]   0.7801465   0.7812219   0.7829069   0.7830044   0.7833641   0.7834737
##  [901]   0.7838130   0.7841026   0.7867847   0.7886151   0.7896421   0.7906656
##  [907]   0.7909752   0.7920344   0.7925415   0.7931039   0.7936289   0.7940073
##  [913]   0.7941960   0.7942207   0.7943376   0.7945351   0.7949089   0.7950589
##  [919]   0.7954381   0.7959382   0.7968087   0.7983656   0.7988792   0.8002204
##  [925]   0.8004623   0.8012656   0.8017529   0.8020776   0.8021792   0.8030062
##  [931]   0.8038735   0.8044499   0.8047333   0.8052833   0.8061435   0.8070430
##  [937]   0.8073446   0.8074020   0.8077862   0.8086956   0.8092365   0.8092485
##  [943]   0.8093043   0.8104545   0.8105970   0.8117159   0.8122833   0.8129451
##  [949]   0.8130414   0.8131405   0.8132601   0.8133188   0.8140390   0.8144882
##  [955]   0.8149419   0.8149925   0.8159958   0.8162729   0.8175117   0.8177298
##  [961]   0.8179039   0.8179791   0.8184564   0.8188923   0.8193312   0.8195626
##  [967]   0.8199032   0.8201534   0.8202064   0.8202353   0.8206214   0.8213134
##  [973]   0.8216586   0.8221469   0.8221767   0.8231532   0.8234968   0.8244505
##  [979]   0.8262599   0.8266728   0.8269204   0.8271919   0.8282918   0.8283330
##  [985]   0.8287709   0.8287968   0.8289144   0.8292146   0.8294321   0.8294498
##  [991]   0.8303896   0.8307441   0.8307683   0.8313645   0.8316558   0.8322682
##  [997]   0.8324496   0.8331097   0.8338075   0.8343683   0.8347659   0.8364015
## [1003]   0.8364800   0.8370371   0.8376577   0.8381507   0.8407316   0.8447110
## [1009]   0.8447255   0.8453770   0.8455298   0.8468037   0.8471627   0.8472286
## [1015]   0.8478946   0.8480085   0.8497094   0.8504785   0.8508322   0.8529298
## [1021]   0.8533119   0.8534380   0.8539122   0.8540821   0.8541645   0.8549627
## [1027]   0.8560053   0.8573821   0.8587681   0.8588455   0.8598208   0.8599371
## [1033]   0.8601054   0.8602344   0.8616748   0.8619009   0.8621112   0.8627906
## [1039]   0.8628122   0.8635418   0.8646582   0.8656309   0.8660176   0.8668410
## [1045]   0.8679619   0.8697297   0.8697472   0.8697968   0.8698365   0.8700123
## [1051]   0.8700650   0.8705890   0.8710329   0.8726448   0.8732383   0.8732817
## [1057]   0.8742390   0.8754162   0.8760416   0.8771325   0.8771905   0.8784774
## [1063]   0.8786810   0.8791307   0.8795107   0.8803549   0.8818419   0.8819313
## [1069]   0.8828674   0.8831068   0.8832272   0.8839057   0.8839430   0.8844095
## [1075]   0.8865652   0.8873162   0.8876094   0.8876097   0.8879364   0.8880269
## [1081]   0.8894016   0.8902534   0.8903489   0.8908086   0.8929190   0.8945545
## [1087]   0.8950292   0.8954016   0.8961583   0.8964922   0.8969051   0.8969787
## [1093]   0.8977710   0.8979557   0.8979898   0.8980390   0.8991128   0.9000252
## [1099]   0.9007652   0.9008054   0.9014428   0.9014642   0.9027737   0.9032069
## [1105]   0.9035311   0.9046027   0.9050126   0.9054103   0.9054456   0.9054959
## [1111]   0.9062094   0.9066786   0.9071990   0.9084307   0.9100115   0.9114225
## [1117]   0.9147136   0.9147482   0.9147567   0.9151964   0.9154164   0.9176975
## [1123]   0.9191865   0.9192542   0.9199036   0.9223626   0.9228028   0.9264187
## [1129]   0.9277507   0.9288620   0.9300858   0.9300930   0.9308648   0.9317625
## [1135]   0.9318011   0.9323545   0.9341834   0.9346445   0.9346497   0.9348797
## [1141]   0.9350591   0.9363101   0.9372962   0.9374483   0.9375062   0.9378156
## [1147]   0.9381002   0.9390691   0.9403512   0.9406167   0.9419768   0.9439814
## [1153]   0.9458320   0.9461854   0.9463323   0.9470196   0.9476587   0.9482092
## [1159]   0.9483598   0.9484787   0.9484864   0.9500165   0.9508692   0.9509736
## [1165]   0.9510580   0.9511175   0.9516131   0.9543279   0.9545429   0.9547443
## [1171]   0.9554912   0.9563161   0.9577317   0.9582201   0.9583789   0.9592188
## [1177]   0.9596947   0.9601905   0.9601923   0.9608883   0.9611581   0.9614579
## [1183]   0.9624915   0.9630935   0.9645697   0.9645921   0.9655337   0.9655774
## [1189]   0.9658942   0.9664572   0.9679634   0.9707428   0.9715779   0.9718427
## [1195]   0.9721034   0.9721131   0.9730049   0.9731113   0.9738585   0.9738784
## [1201]   0.9749304   0.9758571   0.9763416   0.9778621   0.9781126   0.9792017
## [1207]   0.9792169   0.9798268   0.9804299   0.9804722   0.9807982   0.9814008
## [1213]   0.9815395   0.9824445   0.9827863   0.9829542   0.9831671   0.9832184
## [1219]   0.9839800   0.9841682   0.9844787   0.9846993   0.9861015   0.9871999
## [1225]   0.9872320   0.9890139   0.9891864   0.9911653   0.9913988   0.9919343
## [1231]   0.9922498   0.9930176   0.9939195   0.9941734   0.9943025   0.9965391
## [1237]   0.9966786   0.9988840   0.9990466   0.9992926   1.0003026   1.0021116
## [1243]   1.0030468   1.0047025   1.0054915   1.0057376   1.0065163   1.0067643
## [1249]   1.0067699   1.0072598   1.0083161   1.0087018   1.0098236   1.0104439
## [1255]   1.0112747   1.0115052   1.0128923   1.0136669   1.0141601   1.0145871
## [1261]   1.0145897   1.0147240   1.0147376   1.0156779   1.0157732   1.0167663
## [1267]   1.0183310   1.0187734   1.0198151   1.0198519   1.0203721   1.0222429
## [1273]   1.0229554   1.0230696   1.0233197   1.0235946   1.0241707   1.0255577
## [1279]   1.0270338   1.0277699   1.0297738   1.0300100   1.0300459   1.0304098
## [1285]   1.0305522   1.0308853   1.0324743   1.0330723   1.0333103   1.0338815
## [1291]   1.0347292   1.0348075   1.0349140   1.0357268   1.0359398   1.0374703
## [1297]   1.0377482   1.0388364   1.0392213   1.0405074   1.0430246   1.0441164
## [1303]   1.0449127   1.0455850   1.0460215   1.0466317   1.0467116   1.0469027
## [1309]   1.0481177   1.0488440   1.0497110   1.0517261   1.0520642   1.0555481
## [1315]   1.0574452   1.0578468   1.0580621   1.0595243   1.0608892   1.0614195
## [1321]   1.0619367   1.0626534   1.0627080   1.0627990   1.0628534   1.0631119
## [1327]   1.0635883   1.0643174   1.0648992   1.0650121   1.0661107   1.0672341
## [1333]   1.0678749   1.0680066   1.0697864   1.0741863   1.0748755   1.0749784
## [1339]   1.0763685   1.0769091   1.0792139   1.0800708   1.0806208   1.0812567
## [1345]   1.0817457   1.0818835   1.0819152   1.0819546   1.0820133   1.0823307
## [1351]   1.0840158   1.0849023   1.0853968   1.0861082   1.0861628   1.0864227
## [1357]   1.0869858   1.0874022   1.0886233   1.0890866   1.0904448   1.0919304
## [1363]   1.0937159   1.0950022   1.0952554   1.0957835   1.0964840   1.0979811
## [1369]   1.0987403   1.0992247   1.0992315   1.1000039   1.1002391   1.1013775
## [1375]   1.1026304   1.1027366   1.1028884   1.1042691   1.1043195   1.1055237
## [1381]   1.1086549   1.1131017   1.1138909   1.1151416   1.1152046   1.1174117
## [1387]   1.1174186   1.1177210   1.1183843   1.1185025   1.1213730   1.1247056
## [1393]   1.1257261   1.1262225   1.1292490   1.1298665   1.1309039   1.1322571
## [1399]   1.1328745   1.1330408   1.1347715   1.1349432   1.1353753   1.1358820
## [1405]   1.1364431   1.1386272   1.1387587   1.1403302   1.1404228   1.1420097
## [1411]   1.1441132   1.1463518   1.1466089   1.1475143   1.1475730   1.1492941
## [1417]   1.1503238   1.1516628   1.1519296   1.1525550   1.1533898   1.1546714
## [1423]   1.1555424   1.1555453   1.1565593   1.1566682   1.1573865   1.1581806
## [1429]   1.1584128   1.1614027   1.1614269   1.1622568   1.1637738   1.1650323
## [1435]   1.1653463   1.1656880   1.1678587   1.1683905   1.1690676   1.1699073
## [1441]   1.1706660   1.1715697   1.1718249   1.1723033   1.1728936   1.1730046
## [1447]   1.1732179   1.1735953   1.1739925   1.1745378   1.1771560   1.1775441
## [1453]   1.1780537   1.1797450   1.1820034   1.1844041   1.1854435   1.1868073
## [1459]   1.1873928   1.1878781   1.1893119   1.1901639   1.1903660   1.1912268
## [1465]   1.1922176   1.1926333   1.1927902   1.1938147   1.1962577   1.1981495
## [1471]   1.1985143   1.1985592   1.1990461   1.1991275   1.1995200   1.1999519
## [1477]   1.2014258   1.2020362   1.2038118   1.2041783   1.2059218   1.2072504
## [1483]   1.2083849   1.2084293   1.2087268   1.2099515   1.2117004   1.2124104
## [1489]   1.2128650   1.2136927   1.2147264   1.2161839   1.2163150   1.2200792
## [1495]   1.2213760   1.2215103   1.2222150   1.2224025   1.2232022   1.2232602
## [1501]   1.2237422   1.2244234   1.2246315   1.2258755   1.2263274   1.2272824
## [1507]   1.2274066   1.2275329   1.2295792   1.2307251   1.2324780   1.2360625
## [1513]   1.2369252   1.2373274   1.2374776   1.2382874   1.2398477   1.2416535
## [1519]   1.2424545   1.2436524   1.2458027   1.2467566   1.2484418   1.2490162
## [1525]   1.2495251   1.2523647   1.2548452   1.2554274   1.2555548   1.2562986
## [1531]   1.2565529   1.2572272   1.2579633   1.2613796   1.2633257   1.2635152
## [1537]   1.2643135   1.2648953   1.2650368   1.2661860   1.2666744   1.2687481
## [1543]   1.2709757   1.2735285   1.2736494   1.2756235   1.2772494   1.2781034
## [1549]   1.2785381   1.2795886   1.2800241   1.2800406   1.2817326   1.2819541
## [1555]   1.2829440   1.2859882   1.2860742   1.2869872   1.2883833   1.2892867
## [1561]   1.2898550   1.2917478   1.2924151   1.2925132   1.2952029   1.2977750
## [1567]   1.2980554   1.3005139   1.3006650   1.3007460   1.3009317   1.3019108
## [1573]   1.3029487   1.3037416   1.3049984   1.3058234   1.3063048   1.3067561
## [1579]   1.3086955   1.3154814   1.3157941   1.3165069   1.3167836   1.3179420
## [1585]   1.3183128   1.3198638   1.3210494   1.3269609   1.3287206   1.3318451
## [1591]   1.3342740   1.3349397   1.3355628   1.3356592   1.3366280   1.3408722
## [1597]   1.3429692   1.3432889   1.3442026   1.3450673   1.3454883   1.3455432
## [1603]   1.3481846   1.3500621   1.3508930   1.3554631   1.3589260   1.3620920
## [1609]   1.3636627   1.3649376   1.3651556   1.3686199   1.3696722   1.3713594
## [1615]   1.3732902   1.3735053   1.3772325   1.3784412   1.3795371   1.3795942
## [1621]   1.3814474   1.3829251   1.3838569   1.3846428   1.3857183   1.3897211
## [1627]   1.3901185   1.3903952   1.3914051   1.3919411   1.3954015   1.3960868
## [1633]   1.3961494   1.4018472   1.4021056   1.4039238   1.4085773   1.4089678
## [1639]   1.4101737   1.4118522   1.4121592   1.4126702   1.4130630   1.4131667
## [1645]   1.4138053   1.4157711   1.4178521   1.4187727   1.4195717   1.4199811
## [1651]   1.4233572   1.4236697   1.4253488   1.4259968   1.4260486   1.4267522
## [1657]   1.4275042   1.4295438   1.4309956   1.4321371   1.4330809   1.4399243
## [1663]   1.4407096   1.4418439   1.4427453   1.4432190   1.4437418   1.4438016
## [1669]   1.4456521   1.4456730   1.4487773   1.4498902   1.4509150   1.4523621
## [1675]   1.4534811   1.4570276   1.4626462   1.4716815   1.4720143   1.4727136
## [1681]   1.4750172   1.4752694   1.4763282   1.4774566   1.4800187   1.4813485
## [1687]   1.4820112   1.4834483   1.4851707   1.4860584   1.4864585   1.4867025
## [1693]   1.4890042   1.4920782   1.4931229   1.4933747   1.4951437   1.4965059
## [1699]   1.5008830   1.5011818   1.5018938   1.5025491   1.5028357   1.5030821
## [1705]   1.5056858   1.5062979   1.5071564   1.5103364   1.5111724   1.5113727
## [1711]   1.5127681   1.5133059   1.5138474   1.5180594   1.5190044   1.5228436
## [1717]   1.5262343   1.5295433   1.5303003   1.5306857   1.5332281   1.5376315
## [1723]   1.5394887   1.5422913   1.5451451   1.5453773   1.5465554   1.5469524
## [1729]   1.5492449   1.5512944   1.5521963   1.5584811   1.5606261   1.5606598
## [1735]   1.5617033   1.5655089   1.5669691   1.5674678   1.5678869   1.5683463
## [1741]   1.5735705   1.5748865   1.5758837   1.5776904   1.5827061   1.5829671
## [1747]   1.5853224   1.6003652   1.6006164   1.6010863   1.6020551   1.6042015
## [1753]   1.6052779   1.6082992   1.6121857   1.6209937   1.6238177   1.6238344
## [1759]   1.6238996   1.6241730   1.6250326   1.6251262   1.6256465   1.6286073
## [1765]   1.6293859   1.6308965   1.6314172   1.6315983   1.6344405   1.6367661
## [1771]   1.6411350   1.6431842   1.6432949   1.6447440   1.6501074   1.6504058
## [1777]   1.6507636   1.6528441   1.6560412   1.6577178   1.6581265   1.6597456
## [1783]   1.6607213   1.6609102   1.6661388   1.6663671   1.6691407   1.6696525
## [1789]   1.6721620   1.6820360   1.6846066   1.6865434   1.6889176   1.6930991
## [1795]   1.6984720   1.7008520   1.7016805   1.7096092   1.7136466   1.7157790
## [1801]   1.7165590   1.7175880   1.7271617   1.7275531   1.7285506   1.7389740
## [1807]   1.7454352   1.7523719   1.7534853   1.7585402   1.7585604   1.7588329
## [1813]   1.7694932   1.7776066   1.7795162   1.7812217   1.7819125   1.7875866
## [1819]   1.7889339   1.7899365   1.7901456   1.7944671   1.7948225   1.7955777
## [1825]   1.7975224   1.7981327   1.8002356   1.8024061   1.8059971   1.8080864
## [1831]   1.8155705   1.8180895   1.8236906   1.8260580   1.8274076   1.8275148
## [1837]   1.8350814   1.8397183   1.8404805   1.8406855   1.8455768   1.8515209
## [1843]   1.8551967   1.8559672   1.8610174   1.8624208   1.8645605   1.8657388
## [1849]   1.8665972   1.8677048   1.8698392   1.8700164   1.8729554   1.8771517
## [1855]   1.8775915   1.8781755   1.8794078   1.8801192   1.8803785   1.8866979
## [1861]   1.8893232   1.8915454   1.8934853   1.8951396   1.8987542   1.8992750
## [1867]   1.9102980   1.9121268   1.9133796   1.9160454   1.9175789   1.9178513
## [1873]   1.9214565   1.9217978   1.9253228   1.9261299   1.9272068   1.9281402
## [1879]   1.9313350   1.9316360   1.9361894   1.9384404   1.9414024   1.9484093
## [1885]   1.9536026   1.9545779   1.9581116   1.9594009   1.9627919   1.9638633
## [1891]   1.9777290   1.9790932   1.9816245   1.9829934   1.9888067   1.9899495
## [1897]   2.0024603   2.0036402   2.0065323   2.0069631   2.0088237   2.0115375
## [1903]   2.0155715   2.0171262   2.0191473   2.0201080   2.0234297   2.0261072
## [1909]   2.0438230   2.0567678   2.0636313   2.0658300   2.0677668   2.0689835
## [1915]   2.0692007   2.0700957   2.0713258   2.0866379   2.0883402   2.0927396
## [1921]   2.0969616   2.1047230   2.1055757   2.1100394   2.1139683   2.1147829
## [1927]   2.1155144   2.1204372   2.1258424   2.1311731   2.1330866   2.1400710
## [1933]   2.1417963   2.1420682   2.1448374   2.1462064   2.1480565   2.1496460
## [1939]   2.1511025   2.1547767   2.1551235   2.1565596   2.1643176   2.1649402
## [1945]   2.1676541   2.1693250   2.1767428   2.1793480   2.1867110   2.1992557
## [1951]   2.2083865   2.2106034   2.2131498   2.2200281   2.2217600   2.2286257
## [1957]   2.2298974   2.2390440   2.2393015   2.2418520   2.2448694   2.2476892
## [1963]   2.2481490   2.2642734   2.2877960   2.2970873   2.2995314   2.3124699
## [1969]   2.3161273   2.3175565   2.3402208   2.3454942   2.3591721   2.3594162
## [1975]   2.3607938   2.3629115   2.3636761   2.3734334   2.3735555   2.3834169
## [1981]   2.3853514   2.3861121   2.3876009   2.3966971   2.3996039   2.4085088
## [1987]   2.4167299   2.4172439   2.4174765   2.4175322   2.4202989   2.4239986
## [1993]   2.4318210   2.4372540   2.4428654   2.4526638   2.4836319   2.4878418
## [1999]   2.4997693   2.5047015   2.5060349   2.5111601   2.5205294   2.5247558
## [2005]   2.5382656   2.5398301   2.5435299   2.5456429   2.5486967   2.5519215
## [2011]   2.5552796   2.5558080   2.5588329   2.5599484   2.5621150   2.5640541
## [2017]   2.5680290   2.5726923   2.5763707   2.5765995   2.5814477   2.5919966
## [2023]   2.5949313   2.5989147   2.6104946   2.6137039   2.6233350   2.6244647
## [2029]   2.6249021   2.6265465   2.6392170   2.6407169   2.6573517   2.6599641
## [2035]   2.6777222   2.6791668   2.6814275   2.6817859   2.6843435   2.6848772
## [2041]   2.6866188   2.6908301   2.7138315   2.7144258   2.7248559   2.7301569
## [2047]   2.7359845   2.7486347   2.7580230   2.7687816   2.7773295   2.7862940
## [2053]   2.7924538   2.8149050   2.8184045   2.8206959   2.8260915   2.8378468
## [2059]   2.8420757   2.8432878   2.8459755   2.8570101   2.8604739   2.8642130
## [2065]   2.8653104   2.8852788   2.9007960   2.9186248   2.9423761   2.9517922
## [2071]   2.9636901   2.9655866   2.9725784   2.9826863   2.9910800   2.9932650
## [2077]   3.0103506   3.0244801   3.0303243   3.0382426   3.0415988   3.0429840
## [2083]   3.0574260   3.0867455   3.0933206   3.1140658   3.1225182   3.1227603
## [2089]   3.1241297   3.1311504   3.1460197   3.1517578   3.1630106   3.1637972
## [2095]   3.1767311   3.1796823   3.1949022   3.1995226   3.2121238   3.2165786
## [2101]   3.2183231   3.2201877   3.2474577   3.2489856   3.2521060   3.2592743
## [2107]   3.2662510   3.2825903   3.2894529   3.2913257   3.2949023   3.2969356
## [2113]   3.2970257   3.3013525   3.3247556   3.3249054   3.3679460   3.3863611
## [2119]   3.3996622   3.4001593   3.4124408   3.4178616   3.4489398   3.4652033
## [2125]   3.4765205   3.4794751   3.5188086   3.5266922   3.5455007   3.5491084
## [2131]   3.5542591   3.5876405   3.6135678   3.6338087   3.6677072   3.6752350
## [2137]   3.6843044   3.6961164   3.6993319   3.7036778   3.7240977   3.7246246
## [2143]   3.7820345   3.7903513   3.7930644   3.7939586   3.7990345   3.8156025
## [2149]   3.8156793   3.8306291   3.8371117   3.8726525   3.8729742   3.8775006
## [2155]   3.8819237   3.8866782   3.9279117   3.9936977   4.0178850   4.0365251
## [2161]   4.0499507   4.0613106   4.0669474   4.0840432   4.1146182   4.1193782
## [2167]   4.1729019   4.2271076   4.2302465   4.2354411   4.2492793   4.2643778
## [2173]   4.2727063   4.3033916   4.3041744   4.3398677   4.3461774   4.3514905
## [2179]   4.3802115   4.4025093   4.4221213   4.4374787   4.4391075   4.4712035
## [2185]   4.4939646   4.5750358   4.5975297   4.7294520   4.7618201   4.7985029
## [2191]   4.8181275   4.8504575   4.8798306   4.8998115   4.9213187   4.9251375
## [2197]   4.9552067   5.0291743   5.0587383   5.0815809   5.0872854   5.1003976
## [2203]   5.1389420   5.1558399   5.1579564   5.1796469   5.3312483   5.3626316
## [2209]   5.3817887   5.4241578   5.4577165   5.4582250   5.4777764   5.4791407
## [2215]   5.5094493   5.6939869   5.6988444   5.7720164   5.7945188   5.8877661
## [2221]   5.9441077   5.9754978   6.0717683   6.0918880   6.1196793   6.1946549
## [2227]   6.2017318   6.2851962   6.3067197   6.3193443   6.3565358   6.4255585
## [2233]   6.4431615   6.4715959   6.6737212   6.8952237   7.0042314   7.0068910
## [2239]   7.1340845   7.1359970   7.3611680   7.4225371   7.5383580   7.5712922
## [2245]   7.5905989   7.6278969   7.9200891   7.9386557   7.9428632   7.9451998
## [2251]   7.9569757   8.1446161   8.1870313   8.4801644   8.5712445   8.5963497
## [2257]   8.6276438   8.7299346   9.0349994   9.2191881   9.8431754   9.8464939
## [2263]   9.8882455   9.9455643  10.2633079  10.3475786  10.4305757  10.6420559
## [2269]  10.6769504  10.7640623  11.9378255  12.3592579  12.3779762  13.5066361
## [2275]  13.7367796  14.2823862  14.5924310  14.6799347  15.3261713  16.1518716
## [2281]  17.0079064  17.0125443  17.2269594  18.3323575  19.2685358  19.6053300
## [2287]  21.3282581  21.4616139  21.7673517  22.3792081  25.3474192  27.7542633
## [2293]  31.2905447  35.3871840  35.7003598  47.7892125  52.2617451  68.8810473
## [2299] 130.1752467
barplot(cah.ward$height)

Perte d’inertie quand on passe de k à k+1 classes. Au début faible perte d’inertie donc le regroupement est pertinent. La dernière hauteur représente la perte d’inertie inter-classe quand on passe de 2 à 1 classe. La perte est importante donc le regroupement est non pertinent.

Combien de groupes garder ? La perte devient plus importante quand on passe de 4 à 3 classes. Donc on peut garder 4 classes. Si on sépare en 5 classes, alors y aura un groupe très petit.

plot(cah.ward, hang =-1,main="ward.D2",cex=0.2)  
K=4
rect.hclust(cah.ward,K)

groupes.cah <- cutree(cah.ward, K)
groupes.cah
##    [1] 1 2 2 2 2 2 2 1 1 2 2 1 1 1 2 2 2 2 2 2 2 2 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2
##   [38] 2 1 1 1 2 1 2 1 2 2 2 2 1 2 1 2 3 2 2 1 1 2 2 2 2 2 2 2 2 1 1 1 2 1 1 1 3
##   [75] 2 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 4 1 4 4 4
##  [112] 4 1 1 3 2 1 2 2 4 4 4 4 1 1 2 3 3 3 3 3 3 3 3 3 3 4 3 3 1 4 3 4 4 3 3 3 4
##  [149] 4 3 3 4 4 4 2 3 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 4 3 4
##  [186] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 1 3 3 4 4 4 4 4 4 4
##  [223] 4 3 3 4 4 4 4 4 4 3 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 1 4 4 4 3 4 4 4 3 3 3
##  [260] 4 4 3 3 4 4 4 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4
##  [297] 1 1 1 1 3 3 3 4 4 1 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 1 1 3 4 4 4 4 4 4 1 1 3
##  [334] 1 1 3 1 1 1 1 1 1 1 3 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
##  [371] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 3 3 2 2
##  [408] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1 1 2 2 1 1 1 1 2 3 2 2 2 3 3
##  [445] 2 2 2 2 2 2 2 1 3 2 1 3 3 3 3 3 3 3 3 3 3 3 1 4 4 4 4 4 4 4 4 3 2 3 3 4 4
##  [482] 4 3 3 3 3 1 4 3 4 4 3 3 3 4 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
##  [519] 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3
##  [556] 3 3 4 4 4 4 4 4 4 4 4 4 4 3 4 4 3 3 4 4 4 4 4 4 4 4 4 3 4 3 4 4 4 4 4 4 4
##  [593] 4 4 4 4 4 4 4 4 4 4 3 4 3 3 3 3 4 4 4 4 4 4 3 3 3 4 4 4 1 3 4 4 4 4 4 4 4
##  [630] 4 4 3 1 3 3 3 3 3 3 3 4 4 4 4 4 4 4 3 4 4 4 4 1 1 1 4 1 1 2 1 3 1 1 2 1 1
##  [667] 2 2 2 2 3 3 1 1 3 3 2 2 2 2 2 1 1 1 1 1 2 2 1 1 3 3 3 2 2 3 2 2 3 1 1 2 3
##  [704] 2 3 1 1 2 2 2 1 1 2 2 2 2 2 2 2 2 1 1 1 2 3 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2
##  [741] 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 1 2 2 2 1 1 2 2 1 2 2 2 2 1 1 3 2 2 2 2 3
##  [778] 1 2 2 2 2 1 1 1 3 2 2 2 2 2 3 2 2 3 1 1 3 2 1 4 1 4 1 1 1 1 1 1 1 1 1 1 3
##  [815] 1 1 1 3 4 4 4 4 1 1 3 3 1 4 1 4 3 3 4 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4
##  [852] 4 3 3 3 3 4 4 4 4 3 3 3 4 4 4 1 4 4 4 4 4 3 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4
##  [889] 4 4 4 4 3 3 4 4 4 4 3 3 3 3 3 3 4 4 4 3 4 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4
##  [926] 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
##  [963] 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 1 3 3 3 4 3 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 3
## [1000] 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 1 1 1 3 3 3 3 3 3 3 4 4 4 1 1 1 1 2 2 2
## [1037] 1 1 2 1 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 1 2
## [1074] 2 3 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 3 3 2 2 1 2 2 2 1 4 1 1 1 1 3 1 1 3 2 2
## [1111] 1 3 2 2 2 1 1 1 1 1 1 4 1 1 1 1 3 1 3 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 4 3 3
## [1148] 3 3 3 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 3 3 4 4
## [1185] 4 4 3 3 3 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 3 3 3 3 4 4
## [1222] 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3
## [1259] 3 3 4 4 3 4 4 3 3 4 3 4 3 4 3 1 3 3 4 4 4 4 3 3 3 3 3 4 4 3 4 4 3 4 4 4 4
## [1296] 4 4 4 4 4 4 2 3 4 4 4 4 3 1 4 4 4 3 3 3 3 4 4 4 4 4 4 1 3 3 3 3 3 3 3 3 3
## [1333] 2 2 3 1 1 2 3 2 1 2 3 2 1 1 1 1 1 1 3 1 3 2 1 1 1 1 1 1 1 1 1 3 2 2 2 1 1
## [1370] 2 2 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 2 2 3 3 2
## [1407] 2 1 3 1 2 1 1 3 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 1 1 1 1 1 2 1 1 2 1 3 2 3
## [1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 3 2 1 1 2 3 3 3 2 3 2 1 1 1
## [1481] 4 4 1 1 4 1 3 4 4 4 4 3 3 1 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 1 4 4
## [1518] 4 3 4 4 4 4 4 3 3 3 3 3 3 4 4 4 4 3 3 3 4 4 4 4 4 4 3 2 1 4 4 4 3 4 4 4 4
## [1555] 4 4 3 3 3 4 3 4 4 3 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4
## [1592] 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 3 3 3 4 4 3 4 3 3 3 3 4 4 4 4 3 4 4 4 4 4
## [1629] 4 3 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 1 3 3 4 4 4 4 4
## [1666] 4 4 4 4 1 3 1 4 4 2 1 4 4 4 4 4 4 4 4 3 3 4 4 1 3 1 4 4 1 4 4 1 1 1 3 4 4
## [1703] 4 1 4 1 1 1 1 1 1 1 2 2 2 3 2 3 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1740] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2
## [1777] 2 1 1 2 3 3 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1
## [1814] 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 1 4 4 4 4 4 4 1 1 1 1 1 2 2
## [1851] 1 4 4 4 4 1 1 2 2 3 2 1 3 1 1 1 3 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 1 3 3 4
## [1888] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4
## [1925] 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4
## [1962] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4
## [1999] 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 1 3 4 4
## [2036] 4 4 4 4 4 4 1 1 4 1 4 1 3 2 3 4 4 4 1 1 1 2 1 2 3 2 2 2 1 1 1 1 1 1 2 1 1
## [2073] 1 1 2 3 2 3 3 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2
## [2110] 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3
## [2147] 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2
## [2184] 2 2 2 1 1 2 1 1 1 2 3 2 2 2 2 3 1 1 2 1 1 3 2 2 1 1 1 1 2 1 1 2 2 2 2 2 2
## [2221] 3 3 3 1 1 1 1 1 1 1 3 1 4 4 3 3 3 3 3 1 1 4 4 4 4 4 4 3 2 3 3 4 1 4 4 4 4
## [2258] 4 4 4 4 4 3 2 3 3 3 4 4 3 3 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 3 4 3
## [2295] 3 3 3 1 3 4
table(groupes.cah)
## groupes.cah
##   1   2   3   4 
## 387 568 423 922

Interprétation des groupes

for (i in 1:K)
{ cat("groupe", i,"\n")
  I=which(groupes.cah==i)
  print(rownames(data)[I]) }
## groupe 1 
##   [1] "1"    "8"    "9"    "12"   "13"   "14"   "24"   "25"   "39"   "40"  
##  [11] "41"   "43"   "45"   "50"   "52"   "57"   "58"   "67"   "68"   "69"  
##  [21] "71"   "72"   "73"   "76"   "77"   "78"   "79"   "80"   "83"   "84"  
##  [31] "85"   "87"   "88"   "89"   "90"   "95"   "96"   "97"   "98"   "103" 
##  [41] "104"  "105"  "106"  "108"  "113"  "114"  "117"  "124"  "125"  "140" 
##  [51] "213"  "249"  "297"  "298"  "299"  "300"  "306"  "322"  "323"  "331" 
##  [61] "332"  "334"  "335"  "337"  "338"  "339"  "340"  "341"  "342"  "343" 
##  [71] "397"  "422"  "430"  "431"  "434"  "435"  "436"  "437"  "452"  "455" 
##  [81] "467"  "487"  "621"  "633"  "653"  "654"  "655"  "657"  "658"  "660" 
##  [91] "662"  "663"  "665"  "666"  "673"  "674"  "682"  "683"  "684"  "685" 
## [101] "686"  "689"  "690"  "700"  "701"  "706"  "707"  "711"  "712"  "721" 
## [111] "722"  "723"  "753"  "754"  "755"  "757"  "761"  "762"  "765"  "770" 
## [121] "771"  "778"  "783"  "784"  "785"  "796"  "797"  "800"  "802"  "804" 
## [131] "805"  "806"  "807"  "808"  "809"  "810"  "811"  "812"  "813"  "815" 
## [141] "816"  "817"  "823"  "824"  "827"  "829"  "867"  "978"  "1017" "1018"
## [151] "1019" "1030" "1031" "1032" "1033" "1037" "1038" "1040" "1049" "1050"
## [161] "1065" "1066" "1072" "1082" "1083" "1084" "1085" "1087" "1088" "1089"
## [171] "1090" "1095" "1099" "1101" "1102" "1103" "1104" "1106" "1107" "1111"
## [181] "1116" "1117" "1118" "1119" "1120" "1121" "1123" "1124" "1125" "1126"
## [191] "1128" "1274" "1309" "1323" "1336" "1337" "1341" "1345" "1346" "1347"
## [201] "1348" "1349" "1350" "1352" "1355" "1356" "1357" "1358" "1359" "1360"
## [211] "1361" "1362" "1363" "1368" "1369" "1378" "1379" "1380" "1381" "1383"
## [221] "1384" "1385" "1386" "1396" "1397" "1398" "1399" "1400" "1401" "1408"
## [231] "1410" "1412" "1413" "1425" "1430" "1431" "1432" "1433" "1434" "1435"
## [241] "1437" "1438" "1440" "1444" "1445" "1446" "1447" "1448" "1449" "1450"
## [251] "1451" "1452" "1453" "1454" "1455" "1456" "1457" "1458" "1462" "1463"
## [261] "1464" "1465" "1466" "1469" "1470" "1478" "1479" "1480" "1483" "1484"
## [271] "1486" "1494" "1495" "1496" "1497" "1515" "1546" "1658" "1670" "1672"
## [281] "1676" "1689" "1691" "1694" "1697" "1698" "1699" "1704" "1706" "1707"
## [291] "1708" "1709" "1710" "1711" "1712" "1771" "1772" "1778" "1779" "1784"
## [301] "1811" "1812" "1813" "1815" "1816" "1817" "1818" "1819" "1820" "1821"
## [311] "1822" "1823" "1824" "1825" "1826" "1837" "1844" "1845" "1846" "1847"
## [321] "1848" "1851" "1856" "1857" "1862" "1864" "1865" "1866" "1884" "2032"
## [331] "2042" "2043" "2045" "2047" "2054" "2055" "2056" "2058" "2064" "2065"
## [341] "2066" "2067" "2068" "2069" "2071" "2072" "2073" "2074" "2080" "2081"
## [351] "2082" "2083" "2084" "2085" "2086" "2087" "2088" "2089" "2112" "2156"
## [361] "2187" "2188" "2190" "2191" "2192" "2200" "2201" "2203" "2204" "2208"
## [371] "2209" "2210" "2211" "2213" "2214" "2224" "2225" "2226" "2227" "2228"
## [381] "2229" "2230" "2232" "2240" "2241" "2253" "2298"
## groupe 2 
##   [1] "2"    "3"    "4"    "5"    "6"    "7"    "10"   "11"   "15"   "16"  
##  [11] "17"   "18"   "19"   "20"   "21"   "22"   "26"   "27"   "28"   "29"  
##  [21] "30"   "31"   "32"   "33"   "34"   "35"   "36"   "37"   "38"   "42"  
##  [31] "44"   "46"   "47"   "48"   "49"   "51"   "53"   "55"   "56"   "59"  
##  [41] "60"   "61"   "62"   "63"   "64"   "65"   "66"   "70"   "75"   "81"  
##  [51] "82"   "86"   "91"   "92"   "93"   "94"   "99"   "100"  "101"  "102" 
##  [61] "116"  "118"  "119"  "126"  "155"  "345"  "346"  "347"  "348"  "350" 
##  [71] "351"  "352"  "353"  "354"  "355"  "356"  "357"  "358"  "359"  "360" 
##  [81] "361"  "362"  "363"  "364"  "365"  "366"  "367"  "368"  "369"  "370" 
##  [91] "371"  "372"  "373"  "374"  "375"  "376"  "377"  "378"  "379"  "380" 
## [101] "381"  "382"  "383"  "384"  "385"  "387"  "388"  "389"  "390"  "391" 
## [111] "392"  "393"  "394"  "395"  "396"  "398"  "399"  "400"  "401"  "402" 
## [121] "403"  "406"  "407"  "408"  "409"  "410"  "411"  "412"  "413"  "414" 
## [131] "415"  "416"  "417"  "418"  "419"  "420"  "421"  "423"  "424"  "425" 
## [141] "426"  "427"  "428"  "429"  "432"  "433"  "438"  "440"  "441"  "442" 
## [151] "445"  "446"  "447"  "448"  "449"  "450"  "451"  "454"  "477"  "659" 
## [161] "664"  "667"  "668"  "669"  "670"  "677"  "678"  "679"  "680"  "681" 
## [171] "687"  "688"  "694"  "695"  "697"  "698"  "702"  "704"  "708"  "709" 
## [181] "710"  "713"  "714"  "715"  "716"  "717"  "718"  "719"  "720"  "724" 
## [191] "726"  "727"  "728"  "729"  "730"  "731"  "732"  "733"  "734"  "736" 
## [201] "737"  "738"  "739"  "740"  "741"  "742"  "743"  "744"  "745"  "746" 
## [211] "747"  "748"  "749"  "750"  "751"  "752"  "756"  "758"  "759"  "760" 
## [221] "763"  "764"  "766"  "767"  "768"  "769"  "773"  "774"  "775"  "776" 
## [231] "779"  "780"  "781"  "782"  "787"  "788"  "789"  "790"  "791"  "793" 
## [241] "794"  "799"  "1034" "1035" "1036" "1039" "1041" "1042" "1043" "1044"
## [251] "1045" "1046" "1047" "1048" "1051" "1052" "1053" "1054" "1055" "1056"
## [261] "1057" "1058" "1059" "1060" "1061" "1062" "1063" "1064" "1067" "1068"
## [271] "1069" "1070" "1071" "1073" "1074" "1076" "1077" "1078" "1079" "1080"
## [281] "1081" "1086" "1093" "1094" "1096" "1097" "1098" "1109" "1110" "1113"
## [291] "1114" "1115" "1302" "1333" "1334" "1338" "1340" "1342" "1344" "1354"
## [301] "1365" "1366" "1367" "1370" "1371" "1372" "1373" "1374" "1375" "1376"
## [311] "1377" "1382" "1387" "1388" "1389" "1390" "1391" "1392" "1393" "1394"
## [321] "1395" "1402" "1403" "1406" "1407" "1411" "1415" "1416" "1417" "1418"
## [331] "1419" "1420" "1421" "1422" "1423" "1424" "1426" "1427" "1428" "1429"
## [341] "1436" "1439" "1442" "1459" "1460" "1461" "1468" "1471" "1475" "1477"
## [351] "1545" "1675" "1713" "1714" "1715" "1717" "1719" "1720" "1721" "1722"
## [361] "1723" "1725" "1726" "1727" "1728" "1729" "1730" "1731" "1732" "1733"
## [371] "1734" "1735" "1736" "1737" "1738" "1739" "1740" "1741" "1742" "1743"
## [381] "1744" "1745" "1746" "1747" "1748" "1749" "1750" "1751" "1752" "1753"
## [391] "1754" "1756" "1757" "1758" "1759" "1760" "1761" "1762" "1763" "1764"
## [401] "1765" "1766" "1767" "1768" "1769" "1770" "1773" "1774" "1775" "1776"
## [411] "1777" "1780" "1783" "1785" "1786" "1787" "1788" "1789" "1790" "1791"
## [421] "1792" "1793" "1794" "1795" "1796" "1797" "1798" "1799" "1800" "1801"
## [431] "1802" "1803" "1804" "1805" "1806" "1807" "1808" "1809" "1810" "1814"
## [441] "1827" "1828" "1829" "1830" "1831" "1832" "1833" "1834" "1849" "1850"
## [451] "1858" "1859" "1861" "2049" "2057" "2059" "2061" "2062" "2063" "2070"
## [461] "2075" "2077" "2090" "2091" "2092" "2095" "2096" "2097" "2098" "2099"
## [471] "2100" "2101" "2102" "2103" "2105" "2106" "2107" "2108" "2109" "2110"
## [481] "2111" "2113" "2114" "2115" "2116" "2117" "2118" "2119" "2120" "2121"
## [491] "2122" "2123" "2124" "2125" "2126" "2127" "2129" "2130" "2131" "2132"
## [501] "2133" "2134" "2135" "2136" "2137" "2138" "2139" "2140" "2141" "2142"
## [511] "2143" "2144" "2145" "2147" "2148" "2149" "2150" "2151" "2152" "2153"
## [521] "2154" "2155" "2157" "2158" "2159" "2160" "2161" "2162" "2163" "2164"
## [531] "2165" "2166" "2167" "2168" "2169" "2170" "2171" "2174" "2175" "2176"
## [541] "2177" "2178" "2179" "2180" "2181" "2182" "2183" "2184" "2185" "2186"
## [551] "2189" "2193" "2195" "2196" "2197" "2198" "2202" "2206" "2207" "2212"
## [561] "2215" "2216" "2217" "2218" "2219" "2220" "2249" "2264"
## groupe 3 
##   [1] "23"   "54"   "74"   "115"  "127"  "128"  "129"  "130"  "131"  "132" 
##  [11] "133"  "134"  "135"  "136"  "138"  "139"  "142"  "145"  "146"  "147" 
##  [21] "150"  "151"  "156"  "157"  "168"  "169"  "182"  "184"  "201"  "202" 
##  [31] "214"  "215"  "224"  "225"  "232"  "236"  "237"  "238"  "253"  "257" 
##  [41] "258"  "259"  "262"  "263"  "270"  "271"  "272"  "288"  "289"  "301" 
##  [51] "302"  "303"  "307"  "320"  "321"  "324"  "333"  "336"  "344"  "349" 
##  [61] "386"  "404"  "405"  "439"  "443"  "444"  "453"  "456"  "457"  "458" 
##  [71] "459"  "460"  "461"  "462"  "463"  "464"  "465"  "466"  "476"  "478" 
##  [81] "479"  "483"  "484"  "485"  "486"  "489"  "492"  "493"  "494"  "496" 
##  [91] "497"  "498"  "499"  "500"  "501"  "502"  "519"  "520"  "533"  "534" 
## [101] "535"  "536"  "537"  "553"  "554"  "555"  "556"  "557"  "569"  "572" 
## [111] "573"  "583"  "585"  "603"  "605"  "606"  "607"  "608"  "615"  "616" 
## [121] "617"  "622"  "632"  "634"  "635"  "636"  "637"  "638"  "639"  "640" 
## [131] "648"  "661"  "671"  "672"  "675"  "676"  "691"  "692"  "693"  "696" 
## [141] "699"  "703"  "705"  "725"  "735"  "772"  "777"  "786"  "792"  "795" 
## [151] "798"  "814"  "818"  "825"  "826"  "831"  "832"  "834"  "845"  "846" 
## [161] "853"  "854"  "855"  "856"  "861"  "862"  "863"  "873"  "878"  "879" 
## [171] "880"  "881"  "893"  "894"  "899"  "900"  "901"  "902"  "903"  "904" 
## [181] "908"  "910"  "921"  "922"  "937"  "938"  "943"  "963"  "964"  "965" 
## [191] "966"  "967"  "979"  "980"  "981"  "983"  "993"  "994"  "995"  "996" 
## [201] "999"  "1004" "1005" "1020" "1021" "1022" "1023" "1024" "1025" "1026"
## [211] "1075" "1091" "1092" "1105" "1108" "1112" "1127" "1129" "1137" "1138"
## [221] "1139" "1140" "1141" "1142" "1143" "1144" "1146" "1147" "1148" "1149"
## [231] "1150" "1158" "1159" "1170" "1171" "1172" "1173" "1174" "1181" "1182"
## [241] "1187" "1188" "1189" "1192" "1209" "1216" "1217" "1218" "1219" "1225"
## [251] "1226" "1258" "1259" "1260" "1263" "1266" "1267" "1269" "1271" "1273"
## [261] "1275" "1276" "1281" "1282" "1283" "1284" "1285" "1288" "1291" "1303"
## [271] "1308" "1313" "1314" "1315" "1316" "1324" "1325" "1326" "1327" "1328"
## [281] "1329" "1330" "1331" "1332" "1335" "1339" "1343" "1351" "1353" "1364"
## [291] "1404" "1405" "1409" "1414" "1441" "1443" "1467" "1472" "1473" "1474"
## [301] "1476" "1487" "1492" "1493" "1514" "1519" "1525" "1526" "1527" "1528"
## [311] "1529" "1530" "1535" "1536" "1537" "1544" "1550" "1557" "1558" "1559"
## [321] "1561" "1564" "1568" "1569" "1570" "1583" "1600" "1601" "1608" "1609"
## [331] "1610" "1613" "1615" "1616" "1617" "1618" "1623" "1630" "1639" "1640"
## [341] "1651" "1652" "1659" "1660" "1671" "1685" "1686" "1690" "1700" "1716"
## [351] "1718" "1724" "1755" "1781" "1782" "1835" "1836" "1860" "1863" "1867"
## [361] "1875" "1876" "1885" "1886" "1904" "1917" "1918" "1928" "1940" "1950"
## [371] "1951" "1979" "1994" "1999" "2000" "2027" "2028" "2033" "2048" "2050"
## [381] "2060" "2076" "2078" "2079" "2093" "2094" "2104" "2128" "2146" "2172"
## [391] "2173" "2194" "2199" "2205" "2221" "2222" "2223" "2231" "2235" "2236"
## [401] "2237" "2238" "2239" "2248" "2250" "2251" "2263" "2265" "2266" "2267"
## [411] "2270" "2271" "2278" "2279" "2280" "2281" "2282" "2292" "2294" "2295"
## [421] "2296" "2297" "2299"
## groupe 4 
##   [1] "107"  "109"  "110"  "111"  "112"  "120"  "121"  "122"  "123"  "137" 
##  [11] "141"  "143"  "144"  "148"  "149"  "152"  "153"  "154"  "158"  "159" 
##  [21] "160"  "161"  "162"  "163"  "164"  "165"  "166"  "167"  "170"  "171" 
##  [31] "172"  "173"  "174"  "175"  "176"  "177"  "178"  "179"  "180"  "181" 
##  [41] "183"  "185"  "186"  "187"  "188"  "189"  "190"  "191"  "192"  "193" 
##  [51] "194"  "195"  "196"  "197"  "198"  "199"  "200"  "203"  "204"  "205" 
##  [61] "206"  "207"  "208"  "209"  "210"  "211"  "212"  "216"  "217"  "218" 
##  [71] "219"  "220"  "221"  "222"  "223"  "226"  "227"  "228"  "229"  "230" 
##  [81] "231"  "233"  "234"  "235"  "239"  "240"  "241"  "242"  "243"  "244" 
##  [91] "245"  "246"  "247"  "248"  "250"  "251"  "252"  "254"  "255"  "256" 
## [101] "260"  "261"  "264"  "265"  "266"  "267"  "268"  "269"  "273"  "274" 
## [111] "275"  "276"  "277"  "278"  "279"  "280"  "281"  "282"  "283"  "284" 
## [121] "285"  "286"  "287"  "290"  "291"  "292"  "293"  "294"  "295"  "296" 
## [131] "304"  "305"  "308"  "309"  "310"  "311"  "312"  "313"  "314"  "315" 
## [141] "316"  "317"  "318"  "319"  "325"  "326"  "327"  "328"  "329"  "330" 
## [151] "468"  "469"  "470"  "471"  "472"  "473"  "474"  "475"  "480"  "481" 
## [161] "482"  "488"  "490"  "491"  "495"  "503"  "504"  "505"  "506"  "507" 
## [171] "508"  "509"  "510"  "511"  "512"  "513"  "514"  "515"  "516"  "517" 
## [181] "518"  "521"  "522"  "523"  "524"  "525"  "526"  "527"  "528"  "529" 
## [191] "530"  "531"  "532"  "538"  "539"  "540"  "541"  "542"  "543"  "544" 
## [201] "545"  "546"  "547"  "548"  "549"  "550"  "551"  "552"  "558"  "559" 
## [211] "560"  "561"  "562"  "563"  "564"  "565"  "566"  "567"  "568"  "570" 
## [221] "571"  "574"  "575"  "576"  "577"  "578"  "579"  "580"  "581"  "582" 
## [231] "584"  "586"  "587"  "588"  "589"  "590"  "591"  "592"  "593"  "594" 
## [241] "595"  "596"  "597"  "598"  "599"  "600"  "601"  "602"  "604"  "609" 
## [251] "610"  "611"  "612"  "613"  "614"  "618"  "619"  "620"  "623"  "624" 
## [261] "625"  "626"  "627"  "628"  "629"  "630"  "631"  "641"  "642"  "643" 
## [271] "644"  "645"  "646"  "647"  "649"  "650"  "651"  "652"  "656"  "801" 
## [281] "803"  "819"  "820"  "821"  "822"  "828"  "830"  "833"  "835"  "836" 
## [291] "837"  "838"  "839"  "840"  "841"  "842"  "843"  "844"  "847"  "848" 
## [301] "849"  "850"  "851"  "852"  "857"  "858"  "859"  "860"  "864"  "865" 
## [311] "866"  "868"  "869"  "870"  "871"  "872"  "874"  "875"  "876"  "877" 
## [321] "882"  "883"  "884"  "885"  "886"  "887"  "888"  "889"  "890"  "891" 
## [331] "892"  "895"  "896"  "897"  "898"  "905"  "906"  "907"  "909"  "911" 
## [341] "912"  "913"  "914"  "915"  "916"  "917"  "918"  "919"  "920"  "923" 
## [351] "924"  "925"  "926"  "927"  "928"  "929"  "930"  "931"  "932"  "933" 
## [361] "934"  "935"  "936"  "939"  "940"  "941"  "942"  "944"  "945"  "946" 
## [371] "947"  "948"  "949"  "950"  "951"  "952"  "953"  "954"  "955"  "956" 
## [381] "957"  "958"  "959"  "960"  "961"  "962"  "968"  "969"  "970"  "971" 
## [391] "972"  "973"  "974"  "975"  "976"  "977"  "982"  "984"  "985"  "986" 
## [401] "987"  "988"  "989"  "990"  "991"  "992"  "997"  "998"  "1000" "1001"
## [411] "1002" "1003" "1006" "1007" "1008" "1009" "1010" "1011" "1012" "1013"
## [421] "1014" "1015" "1016" "1027" "1028" "1029" "1100" "1122" "1130" "1131"
## [431] "1132" "1133" "1134" "1135" "1136" "1145" "1151" "1152" "1153" "1154"
## [441] "1155" "1156" "1157" "1160" "1161" "1162" "1163" "1164" "1165" "1166"
## [451] "1167" "1168" "1169" "1175" "1176" "1177" "1178" "1179" "1180" "1183"
## [461] "1184" "1185" "1186" "1190" "1191" "1193" "1194" "1195" "1196" "1197"
## [471] "1198" "1199" "1200" "1201" "1202" "1203" "1204" "1205" "1206" "1207"
## [481] "1208" "1210" "1211" "1212" "1213" "1214" "1215" "1220" "1221" "1222"
## [491] "1223" "1224" "1227" "1228" "1229" "1230" "1231" "1232" "1233" "1234"
## [501] "1235" "1236" "1237" "1238" "1239" "1240" "1241" "1242" "1243" "1244"
## [511] "1245" "1246" "1247" "1248" "1249" "1250" "1251" "1252" "1253" "1254"
## [521] "1255" "1256" "1257" "1261" "1262" "1264" "1265" "1268" "1270" "1272"
## [531] "1277" "1278" "1279" "1280" "1286" "1287" "1289" "1290" "1292" "1293"
## [541] "1294" "1295" "1296" "1297" "1298" "1299" "1300" "1301" "1304" "1305"
## [551] "1306" "1307" "1310" "1311" "1312" "1317" "1318" "1319" "1320" "1321"
## [561] "1322" "1481" "1482" "1485" "1488" "1489" "1490" "1491" "1498" "1499"
## [571] "1500" "1501" "1502" "1503" "1504" "1505" "1506" "1507" "1508" "1509"
## [581] "1510" "1511" "1512" "1513" "1516" "1517" "1518" "1520" "1521" "1522"
## [591] "1523" "1524" "1531" "1532" "1533" "1534" "1538" "1539" "1540" "1541"
## [601] "1542" "1543" "1547" "1548" "1549" "1551" "1552" "1553" "1554" "1555"
## [611] "1556" "1560" "1562" "1563" "1565" "1566" "1567" "1571" "1572" "1573"
## [621] "1574" "1575" "1576" "1577" "1578" "1579" "1580" "1581" "1582" "1584"
## [631] "1585" "1586" "1587" "1588" "1589" "1590" "1591" "1592" "1593" "1594"
## [641] "1595" "1596" "1597" "1598" "1599" "1602" "1603" "1604" "1605" "1606"
## [651] "1607" "1611" "1612" "1614" "1619" "1620" "1621" "1622" "1624" "1625"
## [661] "1626" "1627" "1628" "1629" "1631" "1632" "1633" "1634" "1635" "1636"
## [671] "1637" "1638" "1641" "1642" "1643" "1644" "1645" "1646" "1647" "1648"
## [681] "1649" "1650" "1653" "1654" "1655" "1656" "1657" "1661" "1662" "1663"
## [691] "1664" "1665" "1666" "1667" "1668" "1669" "1673" "1674" "1677" "1678"
## [701] "1679" "1680" "1681" "1682" "1683" "1684" "1687" "1688" "1692" "1693"
## [711] "1695" "1696" "1701" "1702" "1703" "1705" "1838" "1839" "1840" "1841"
## [721] "1842" "1843" "1852" "1853" "1854" "1855" "1868" "1869" "1870" "1871"
## [731] "1872" "1873" "1874" "1877" "1878" "1879" "1880" "1881" "1882" "1883"
## [741] "1887" "1888" "1889" "1890" "1891" "1892" "1893" "1894" "1895" "1896"
## [751] "1897" "1898" "1899" "1900" "1901" "1902" "1903" "1905" "1906" "1907"
## [761] "1908" "1909" "1910" "1911" "1912" "1913" "1914" "1915" "1916" "1919"
## [771] "1920" "1921" "1922" "1923" "1924" "1925" "1926" "1927" "1929" "1930"
## [781] "1931" "1932" "1933" "1934" "1935" "1936" "1937" "1938" "1939" "1941"
## [791] "1942" "1943" "1944" "1945" "1946" "1947" "1948" "1949" "1952" "1953"
## [801] "1954" "1955" "1956" "1957" "1958" "1959" "1960" "1961" "1962" "1963"
## [811] "1964" "1965" "1966" "1967" "1968" "1969" "1970" "1971" "1972" "1973"
## [821] "1974" "1975" "1976" "1977" "1978" "1980" "1981" "1982" "1983" "1984"
## [831] "1985" "1986" "1987" "1988" "1989" "1990" "1991" "1992" "1993" "1995"
## [841] "1996" "1997" "1998" "2001" "2002" "2003" "2004" "2005" "2006" "2007"
## [851] "2008" "2009" "2010" "2011" "2012" "2013" "2014" "2015" "2016" "2017"
## [861] "2018" "2019" "2020" "2021" "2022" "2023" "2024" "2025" "2026" "2029"
## [871] "2030" "2031" "2034" "2035" "2036" "2037" "2038" "2039" "2040" "2041"
## [881] "2044" "2046" "2051" "2052" "2053" "2233" "2234" "2242" "2243" "2244"
## [891] "2245" "2246" "2247" "2252" "2254" "2255" "2256" "2257" "2258" "2259"
## [901] "2260" "2261" "2262" "2268" "2269" "2272" "2273" "2274" "2275" "2276"
## [911] "2277" "2283" "2284" "2285" "2286" "2287" "2288" "2289" "2290" "2291"
## [921] "2293" "2300"

Caractéristiques de chaque groupe.

Means_groupes <- matrix(NA, nrow=K, ncol=dim(data)[2])
colnames(Means_groupes)=colnames(data)
rownames(Means_groupes) =1:K
for (i in 1:K) 
  Means_groupes[i,]<- colMeans(data[groupes.cah==i,])
round(Means_groupes)
##   MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am Pressure3pm
## 1      18      23        1          65          63        1019        1017
## 2      20      25        3          78          74        1014        1013
## 3      17      21        9          81          78        1013        1011
## 4      14      19        2          65          62        1022        1020
##   Temp9am Temp3pm AvgTemp
## 1      21      22      21
## 2      23      24      23
## 3      19      20      19
## 4      17      18      17

Les groupes sont séparés selon la température: groupe 1 : AvgTemp = 21 groupe 2 : AvgTemp = 23 groupe 3 : AvgTemp = 19 groupe 4 : AvgTemp = 17

Kmeans

Avec K=4 classes d’après la CAH

kmeans.result <- kmeans(data.cr,centers=K)
kmeans.result
## K-means clustering with 4 clusters of sizes 612, 438, 415, 835
## 
## Cluster means:
##      MinTemp    MaxTemp    Rainfall Humidity9am Humidity3pm Pressure9am
## 1  0.4660997  0.6837587 -0.26133620  -0.4169394  -0.4055712   0.1295143
## 2  1.3350061  1.2353981  0.01248747   0.8413376   0.8374997  -0.8277244
## 3 -0.1612103 -0.4072096  0.73852561   0.8788391   0.8247842  -0.8010838
## 4 -0.9617766 -0.9467937 -0.18205974  -0.5725236  -0.5519769   0.7374016
##   Pressure3pm    Temp9am    Temp3pm    AvgTemp
## 1   0.1657267  0.6658335  0.6774093  0.5921291
## 2  -0.7870284  1.2224378  1.2079724  1.3275937
## 3  -0.8710366 -0.3836626 -0.4199530 -0.2917815
## 4   0.7242801 -0.9385603 -0.9214202 -0.9853649
## 
## Clustering vector:
##    [1] 1 1 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1
##   [38] 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 2 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1
##   [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 3 1 2 2 1 1 1 1 1 1 1 1 1
##  [112] 1 1 1 2 1 1 1 1 1 1 4 4 1 1 3 3 3 3 3 3 3 3 3 3 3 1 3 3 1 4 3 3 4 3 3 3 4
##  [149] 4 3 3 1 4 4 3 3 3 4 4 3 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 3 4 4 4 4 4 3 4
##  [186] 4 4 3 4 4 4 4 4 4 4 3 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 1 3 3 4 4 3 4 4 4 4
##  [223] 4 3 3 4 4 3 4 4 4 3 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 1 1 3 4 4 3 3 4 4 3 3 3
##  [260] 4 4 4 3 4 4 4 4 4 3 3 3 2 4 4 4 4 4 4 4 1 1 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4
##  [297] 1 1 1 1 3 3 3 4 4 1 3 4 4 4 4 4 4 4 4 4 4 4 3 3 3 1 1 3 4 4 4 4 4 3 1 1 3
##  [334] 1 1 3 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
##  [371] 2 2 2 2 1 2 1 2 2 2 2 2 2 1 2 3 2 2 1 2 2 2 2 1 2 1 1 2 2 1 1 2 2 2 2 2 2
##  [408] 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 3 1 1 1 1 1 1 1 1 1 2 2 2 2 3 3
##  [445] 2 2 2 2 2 2 1 1 3 2 1 3 3 3 3 3 1 3 3 1 1 3 1 4 4 4 4 4 4 4 1 3 3 3 3 4 4
##  [482] 4 3 3 3 3 1 4 4 3 4 3 3 3 4 3 3 3 3 3 3 3 3 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4
##  [519] 3 3 4 4 4 3 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3
##  [556] 3 3 4 4 4 4 4 4 4 3 4 4 4 3 3 4 4 3 4 4 4 4 4 4 4 4 4 3 4 3 3 3 4 4 4 4 4
##  [593] 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 4 4 4 3 3 3 3 4 4 4 1 3 4 4 4 4 4 4 4
##  [630] 4 4 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 1 3 4 4 4 4 1 1 1 4 1 1 1 1 1 1 1 1 1 1
##  [667] 1 2 2 2 3 3 1 1 2 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 3 3 3 2 2 2 2 2 3 1 1 2 2
##  [704] 1 1 1 1 2 2 1 1 1 3 2 2 2 2 2 2 2 1 1 1 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1
##  [741] 1 1 2 1 2 2 2 2 2 2 2 2 1 1 1 1 1 1 2 2 1 1 1 1 1 2 2 2 1 1 1 2 2 2 2 2 3
##  [778] 1 2 2 2 1 1 1 1 3 2 2 2 2 2 2 2 3 2 1 1 2 2 1 4 1 4 1 1 1 1 1 1 1 1 1 1 2
##  [815] 1 1 1 3 3 4 4 4 1 3 3 3 1 4 1 1 4 3 4 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4
##  [852] 4 3 3 3 3 4 4 4 4 3 3 3 4 4 4 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4
##  [889] 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4
##  [926] 4 4 4 3 4 4 4 4 4 4 4 3 3 4 4 4 4 3 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4
##  [963] 3 3 3 3 3 4 3 4 4 4 4 4 4 4 4 4 3 3 3 4 3 3 4 4 4 4 4 4 4 4 3 3 3 3 4 4 3
## [1000] 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 1 1 1 1 3 3 3 3 3 3 4 1 1 1 1 1 1 2 2 1
## [1037] 1 1 2 1 1 2 2 1 1 2 1 1 1 1 2 1 2 2 2 2 2 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## [1074] 1 2 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 1 2 2 1 1 2 2 1 1 1 1 1 1 1 3 1 1 3 3 2
## [1111] 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 3 1 3 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3
## [1148] 3 3 3 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 3 3 4 4
## [1185] 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 3 3 3 3 4 4
## [1222] 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3
## [1259] 3 3 4 4 3 4 4 3 3 3 4 3 3 4 3 3 3 3 4 4 4 4 1 3 3 3 3 4 4 3 4 4 3 4 4 4 4
## [1296] 4 4 4 4 4 1 1 3 3 4 4 4 3 1 4 4 4 4 4 4 1 4 4 4 1 1 1 1 3 2 2 3 3 3 3 3 3
## [1333] 2 2 2 3 1 1 2 3 1 2 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1
## [1370] 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 3 2 2 2 2 2 2 1 1 1 1 1 1 1 2 3 3 2
## [1407] 2 1 1 1 2 1 1 1 2 2 2 2 2 2 2 2 2 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 2 1
## [1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 2 2 2 2 2 2 1 1 1 1
## [1481] 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 1 4 4
## [1518] 3 3 4 4 4 4 4 3 3 3 3 3 3 3 3 3 4 3 3 3 4 4 4 4 4 4 3 3 4 4 4 4 3 4 4 4 4
## [1555] 4 4 3 3 3 4 3 4 3 4 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 3 4 4 4 4 4 4 4
## [1592] 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 3 3 3 3 3 3 3 4 3 3 3 3 4 4 4 4 3 3 4 4 4 4
## [1629] 4 3 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 1 3 3 4 4 4 4 4
## [1666] 4 4 4 4 1 1 1 4 1 1 1 3 4 4 4 1 4 4 4 1 4 4 4 1 2 1 1 4 1 1 1 1 1 1 1 1 1
## [1703] 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 2 1 2 2 3 3 2 2 2 2 2 1 2 2 2 2 1 2 1 1 2
## [1740] 1 2 2 1 1 1 1 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1
## [1777] 1 1 1 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 1 1 1 1
## [1814] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2
## [1851] 1 1 1 4 1 1 1 2 2 2 2 1 4 1 1 1 3 4 4 4 4 4 4 4 1 3 4 4 4 4 4 4 4 1 3 1 4
## [1888] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4
## [1925] 4 4 4 3 3 4 3 3 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4
## [1962] 4 4 4 4 4 4 4 4 4 4 4 4 4 1 3 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 3
## [1999] 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4
## [2036] 4 4 3 4 4 4 1 1 3 4 4 1 2 2 3 4 4 4 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1
## [2073] 1 1 1 2 2 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1
## [2110] 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2147] 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 3 2 2 1 1 1 1 2 2 2 2
## [2184] 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 2 3 3 2
## [2221] 2 2 3 1 1 1 1 1 1 1 1 1 3 1 3 1 3 1 3 1 1 4 4 4 4 4 4 3 3 3 3 3 1 4 4 4 4
## [2258] 4 4 4 4 4 3 3 3 3 3 4 4 3 3 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 3 4 3
## [2295] 3 3 3 3 4 3
## 
## Within cluster sum of squares by cluster:
## [1] 1755.488 1789.869 3423.281 2972.634
##  (between_SS / total_SS =  56.8 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"
kmeans.result <- kmeans(data.cr,centers=K)
kmeans.result$size
## [1] 468 760 641 431

Les résultats changent car sont dépendants de l’initialisation —> choisir une bonne initialisation (avec CAH par exemple) ou stabiliser le problème du choix de l’initialisation en lançant plusieurs kmeans.

Initialisation avec CAH

init <- matrix(NA, nrow=K, ncol=dim(data)[2])
colnames(init)=colnames(data)
for (i in 1:K) init[i,] <- colMeans(data.cr[groupes.cah==i,])
init
##           MinTemp    MaxTemp    Rainfall Humidity9am Humidity3pm Pressure9am
## [1,]  0.395316840  0.5953474 -0.27315886  -0.4880411  -0.4196290   0.2330355
## [2,]  1.220316283  1.2090205 -0.01216608   0.5702286   0.4895641  -0.6750940
## [3,] -0.008041669 -0.2280792  0.56968186   0.8280126   0.8154354  -0.8037610
## [4,] -0.914019132 -0.8900711 -0.13921108  -0.5263203  -0.4995718   0.6868325
##      Pressure3pm    Temp9am    Temp3pm    AvgTemp
## [1,]   0.2623958  0.5931137  0.5957677  0.5100666
## [2,]  -0.6247817  1.1791527  1.1892963  1.2541762
## [3,]  -0.8574065 -0.1918281 -0.2432001 -0.1204129
## [4,]   0.6681256 -0.8873649 -0.8711591 -0.9314894

Attention à bien prendre l’init avec colMeans sur les données centrées réduites parce qu’on lance kmeans sur les données centrées réduites (et sinon problème d’échelle : les centres des classes ne sont pas adaptés)

kmeans.initCAH <- kmeans(data.cr, centers= init)

Stabilisation en lançant plusieurs initialisations

kmeans.result <- kmeans(data.cr,centers=K,nstart=1000)

Comparaison

table(groupes.cah, kmeans.initCAH$cluster)
##            
## groupes.cah   1   2   3   4
##           1 377   0   6   4
##           2 156 394  18   0
##           3  29  44 331  19
##           4  50   0  60 812
table(groupes.cah,kmeans.result$cluster)
##            
## groupes.cah   1   2   3   4
##           1   0   3 369  15
##           2 354   0 209   5
##           3  77   7  23 316
##           4   0 750  40 132
table(kmeans.initCAH$cluster,kmeans.result$cluster)
##    
##       1   2   3   4
##   1   1   6 585  20
##   2 384   0  54   0
##   3  46   0   2 367
##   4   0 754   0  81

On retrouve ici les mêmes groupes avec kmeans initialisé en CAH et kmeans avec plusieurs initialiations (à label switching près sur les groupes).

Sans a-priori sur le choix de K avec la CAH, comment choisir K ?

#Evaluer la proportion d’inertie intra-classe
inertie.intra <- rep(0,times=10)
for (k in 1:10){
kmeans.result <- kmeans(data.cr,centers=k,nstart=100)
inertie.intra[k] <- kmeans.result$tot.withinss/kmeans.result$totss
}
## Warning: did not converge in 10 iterations

## Warning: did not converge in 10 iterations
# Graphique
plot(1:10,inertie.intra,type="b",xlab="Nb. de groupes",ylab="% inertie intra")

À partir de K = 4 classes, l’ajout d’un groupe supplémentaire ne diminue pas “significativement” la part d’inertie intra.

Interprétation des classes avec une ACP

kmeans.result <- kmeans(data.cr,centers=K,nstart=1000)
pairs(data, col=kmeans.result$cluster )

ACP

res=PCA(data,scale.unit=TRUE, graph=FALSE)
res$eig
##           eigenvalue percentage of variance cumulative percentage of variance
## comp 1  5.537506e+00           5.537506e+01                          55.37506
## comp 2  2.132117e+00           2.132117e+01                          76.69623
## comp 3  1.040299e+00           1.040299e+01                          87.09922
## comp 4  7.680060e-01           7.680060e+00                          94.77928
## comp 5  2.985329e-01           2.985329e+00                          97.76461
## comp 6  1.438896e-01           1.438896e+00                          99.20350
## comp 7  3.718915e-02           3.718915e-01                          99.57539
## comp 8  2.658717e-02           2.658717e-01                          99.84126
## comp 9  1.587356e-02           1.587356e-01                         100.00000
## comp 10 1.578246e-28           1.578246e-27                         100.00000
plot(res, choix="var")

axe 1 indique l’importance de la température axe 2 indique l’importance de la pression contre d’humidité

#Plot selon la Température moyenne

plot(res, choix="ind", habillage=10)

#Meth 1 : obtenir le graphe à la main :
plot(res$ind$coord[,1], res$ind$coord[,2], col=kmeans.result$cluster, cex=res$ind$cos2, ylim=c(-4,4))
abline(h=0)
abline(v=0)

Meth 2: en rajoutant la classe au data frame, en lancant une ACP avec la classe comme variable qualitative supplémentaire, et en utilisant l’option habillage de plot :

data.Avecclasse = cbind.data.frame(data, classe = factor(kmeans.result$cluster))
head(data.Avecclasse)
##   MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am Pressure3pm
## 1    18.6    24.5      0.0          53          55      1021.5      1019.6
## 2    19.3    25.2      0.0          77          73      1019.2      1017.6
## 3    20.7    26.4      0.0          73          70      1016.9      1015.4
## 4    20.2    26.7      0.0          70          65      1015.4      1015.0
## 5    20.9    24.7      0.0          85          79      1017.8      1017.1
## 6    19.5    24.9      0.8          82          68      1018.7      1017.6
##   Temp9am Temp3pm AvgTemp classe
## 1    22.4    23.4   21.55      4
## 2    22.5    23.4   22.25      4
## 3    23.8    24.2   23.55      1
## 4    23.5    25.4   23.45      4
## 5    22.5    23.2   22.80      1
## 6    21.2    23.3   22.20      4
dim(data.Avecclasse)
## [1] 2300   11
res=PCA(data.Avecclasse,scale.unit=TRUE, quali.sup = 11, graph=FALSE)
plot(res, choix="ind", habillage=11, cex=0.7, select= "cos2 0.7")

Classe 1 : Température moyenne élevée Classe 2 : Température moyenne faible Classe 3 : Température moyenne-moyenne, Humidité faible, Pression élevée Classe 4: Température moyenne-moyenne, Humidité forte, Pression faible

Silhouette

sil= silhouette(kmeans.result$cluster,dist(data.cr))
rownames(sil)=rownames(data)
sil
##      cluster neighbor     sil_width
## 1          4        1  0.5071893662
## 2          4        1  0.2500491350
## 3          1        4 -0.0884206575
## 4          4        1  0.1426632988
## 5          1        4  0.0670352799
## 6          4        1  0.2485626869
## 7          4        1  0.3918536023
## 8          4        1  0.4410930790
## 9          4        1  0.4310854814
## 10         4        1  0.4497186587
## 11         1        4  0.1193733387
## 12         4        1  0.4148779534
## 13         4        3  0.4213309813
## 14         4        1  0.4869277547
## 15         4        1  0.3109118416
## 16         4        1  0.3285003172
## 17         4        1  0.3303597737
## 18         4        1  0.1711168818
## 19         1        4  0.2529182936
## 20         1        4  0.2243790138
## 21         1        4 -0.0050342693
## 22         4        1  0.1975060581
## 23         4        1  0.2084571428
## 24         4        1  0.4510030690
## 25         4        1  0.4406232744
## 26         4        1  0.3730579499
## 27         4        1  0.3336146936
## 28         4        1  0.1755701461
## 29         1        4  0.1805966632
## 30         1        4  0.0579608698
## 31         4        1  0.1855736516
## 32         4        1  0.1391913421
## 33         1        4  0.2103546790
## 34         1        4  0.2992491829
## 35         1        4 -0.1080846030
## 36         4        1  0.1217148516
## 37         4        1  0.2800606485
## 38         4        1  0.1858821424
## 39         4        1  0.3450954997
## 40         4        1  0.3661685822
## 41         4        1  0.5071918053
## 42         4        1  0.4428702580
## 43         4        1  0.4181515174
## 44         4        1  0.2715009881
## 45         4        1  0.3566716419
## 46         4        1  0.3923865580
## 47         4        1  0.2762158466
## 48         1        4  0.2288758177
## 49         4        1  0.2350413013
## 50         4        1  0.4495574870
## 51         4        1  0.1788504702
## 52         4        1  0.3681266544
## 53         4        1  0.3508580932
## 54         1        4  0.0717663082
## 55         1        4  0.0290120867
## 56         1        4 -0.0528987909
## 57         4        1  0.3580276793
## 58         4        1  0.3909747812
## 59         4        1  0.1350833735
## 60         1        4  0.2969041896
## 61         1        4  0.0916012648
## 62         4        1  0.2275390006
## 63         4        1  0.3691566001
## 64         4        1  0.3434648909
## 65         4        1  0.2639309167
## 66         4        1  0.4442835441
## 67         4        1  0.4798817926
## 68         4        1  0.4792693642
## 69         4        1  0.4768752639
## 70         4        1  0.2779802672
## 71         4        3  0.4206490805
## 72         4        3  0.4805554188
## 73         4        2  0.3954891395
## 74         4        1  0.2561268378
## 75         4        1  0.5162786213
## 76         4        1  0.5068782082
## 77         4        3  0.4040760908
## 78         4        3  0.3696986936
## 79         4        3  0.3661271121
## 80         4        1  0.4475476797
## 81         4        1  0.4200400824
## 82         4        1  0.3649901839
## 83         4        1  0.4148633543
## 84         4        1  0.4544019340
## 85         4        1  0.4510126752
## 86         4        1  0.4187205694
## 87         4        1  0.3855529225
## 88         4        1  0.4109400532
## 89         4        1  0.3594807905
## 90         4        1  0.4825471030
## 91         4        1  0.4259570568
## 92         4        1  0.2055160328
## 93         4        1  0.2128138476
## 94         1        4  0.1895919245
## 95         4        2  0.4105202147
## 96         4        3  0.4335024279
## 97         4        3  0.2960628147
## 98         4        1  0.4434991040
## 99         1        4 -0.0047277421
## 100        4        1  0.3500544324
## 101        4        1  0.2217347557
## 102        1        4  0.2079932154
## 103        4        1  0.2109600279
## 104        4        1  0.4748982200
## 105        4        3  0.4530580329
## 106        4        3  0.4021263470
## 107        4        3  0.2116003251
## 108        4        3  0.4641861345
## 109        4        3  0.2143633309
## 110        4        3  0.1960488134
## 111        4        3  0.1037744277
## 112        4        3  0.1694086079
## 113        4        3  0.2897758878
## 114        4        3  0.3745484902
## 115        1        2  0.0747296955
## 116        4        1  0.1554913479
## 117        4        2  0.3690323019
## 118        4        1  0.2371154417
## 119        4        1  0.3102993621
## 120        4        2  0.2851043530
## 121        3        4  0.0018158611
## 122        3        4  0.3007524542
## 123        3        4  0.1011120262
## 124        4        3  0.3178866642
## 125        4        2  0.1784938946
## 126        1        2  0.0587813584
## 127        1        4 -0.0092006837
## 128        2        1  0.0679208795
## 129        2        1  0.2194547780
## 130        1        2  0.0778027617
## 131        2        4  0.0379037261
## 132        2        4 -0.0108570664
## 133        2        4  0.0905762106
## 134        2        4  0.2533311343
## 135        2        4  0.2377205513
## 136        2        3  0.2060838128
## 137        4        3  0.0773729296
## 138        2        4  0.2014118703
## 139        2        4  0.1918154011
## 140        4        3  0.1455400967
## 141        2        3 -0.0055782803
## 142        2        4  0.0997359743
## 143        2        3  0.2694733595
## 144        2        3  0.0261862551
## 145        2        3  0.3617968955
## 146        2        1  0.1225232861
## 147        2        4  0.2171464818
## 148        3        2  0.4782537239
## 149        2        3  0.0326974820
## 150        2        1  0.1227013425
## 151        1        4 -0.0098638340
## 152        2        4 -0.0740510100
## 153        2        3  0.0289445673
## 154        2        3 -0.0235062913
## 155        1        2  0.0450021008
## 156        2        1  0.0449314377
## 157        2        4  0.2544270325
## 158        2        3 -0.0775363052
## 159        3        2  0.2316916203
## 160        2        3  0.0887917102
## 161        3        2  0.1863027530
## 162        3        2  0.2203322340
## 163        3        2  0.1774621699
## 164        3        2  0.5375337581
## 165        3        2  0.5171572331
## 166        3        2  0.5109468240
## 167        3        2  0.3468876309
## 168        2        3  0.2849213917
## 169        2        3  0.3403240284
## 170        2        3 -0.0409237737
## 171        3        2  0.0549544459
## 172        2        3 -0.0069719320
## 173        3        2  0.4459318032
## 174        3        2  0.5240842551
## 175        3        2  0.5254192006
## 176        3        2  0.5237539879
## 177        3        2  0.4847067631
## 178        2        3  0.2154917421
## 179        3        2  0.3843049942
## 180        3        2  0.5306029535
## 181        3        2  0.5044460040
## 182        2        3 -0.0254779525
## 183        3        2  0.4307688622
## 184        2        3  0.2105154223
## 185        2        3 -0.0404372318
## 186        3        2  0.2285350600
## 187        3        2  0.4257133162
## 188        2        3  0.0464504680
## 189        3        2  0.4969380810
## 190        3        2  0.3904924565
## 191        3        2  0.4837509050
## 192        3        2  0.3441001218
## 193        3        2  0.5093054750
## 194        3        2  0.4986917500
## 195        3        2  0.2909649929
## 196        2        3  0.0810907964
## 197        3        2  0.2156257315
## 198        3        2  0.5311811533
## 199        3        2  0.2788079918
## 200        3        2  0.1225966408
## 201        2        3  0.3305858741
## 202        2        3  0.2240620210
## 203        3        2  0.4192113564
## 204        3        2  0.5153542828
## 205        3        2  0.3269473275
## 206        3        2  0.4974781450
## 207        3        2  0.4658767010
## 208        3        2  0.4898643602
## 209        3        2  0.4862980661
## 210        3        2  0.4699210077
## 211        3        4  0.4479082560
## 212        3        4  0.1412552009
## 213        4        2  0.1114151238
## 214        2        4  0.3846130087
## 215        2        3  0.2453496539
## 216        3        2  0.4687798288
## 217        3        2  0.2164488661
## 218        2        3  0.2281040465
## 219        3        2  0.2579895945
## 220        3        2  0.5225980095
## 221        3        2  0.4787943949
## 222        3        2  0.5160164498
## 223        2        3 -0.0625169397
## 224        2        1  0.1260787832
## 225        2        3  0.2981279376
## 226        3        2  0.2767955344
## 227        2        3  0.0227994335
## 228        2        3  0.1914224246
## 229        3        2  0.5278855487
## 230        3        2  0.5357939273
## 231        3        2  0.2011659906
## 232        2        4  0.3585779975
## 233        3        2  0.2121423186
## 234        3        2  0.5099628372
## 235        3        2  0.1585141118
## 236        2        3  0.3402491167
## 237        2        3  0.3658297536
## 238        2        3  0.2490442975
## 239        3        2  0.1686692814
## 240        3        2  0.3917375807
## 241        3        2  0.3838895721
## 242        3        2  0.3729269768
## 243        3        2  0.5126910630
## 244        3        2  0.5252380448
## 245        3        2  0.1464977459
## 246        3        2  0.5064918533
## 247        3        4  0.4555713512
## 248        4        3  0.0466045617
## 249        4        2  0.1243470959
## 250        2        3  0.1108538702
## 251        3        2  0.4184337053
## 252        3        2  0.2725404125
## 253        2        1  0.2778655368
## 254        2        3  0.1415769757
## 255        3        2  0.4979358398
## 256        3        2  0.3914211501
## 257        2        3  0.2610206719
## 258        2        4  0.2186540200
## 259        2        3  0.2738564510
## 260        3        2  0.3716198919
## 261        3        2  0.1954243682
## 262        2        3  0.0423588001
## 263        2        3  0.1248126357
## 264        3        2  0.3405409012
## 265        3        2  0.4965295055
## 266        3        4  0.5239039907
## 267        3        4  0.4973743843
## 268        3        2  0.2137994876
## 269        2        3  0.2032125206
## 270        2        4  0.2076486325
## 271        2        1  0.1539570767
## 272        1        4 -0.0115176383
## 273        2        3 -0.0225477198
## 274        3        2  0.4140659324
## 275        3        2  0.4832570676
## 276        3        4  0.5031475187
## 277        3        2  0.3459277382
## 278        3        2  0.3513490426
## 279        3        2  0.2796938539
## 280        2        4 -0.0445630981
## 281        4        3  0.0852337814
## 282        3        4  0.0339220685
## 283        3        4  0.4572620610
## 284        3        2  0.5053612405
## 285        3        2  0.3475298548
## 286        3        2  0.2670776413
## 287        2        3 -0.0492416058
## 288        2        4  0.0503954028
## 289        2        4  0.2192171065
## 290        3        4  0.2675845276
## 291        3        2  0.4251333263
## 292        3        2  0.4847797146
## 293        3        2  0.5463981719
## 294        3        4  0.5091049241
## 295        3        2  0.4547368118
## 296        2        3 -0.0688241825
## 297        4        2  0.1137233437
## 298        4        2  0.2115136092
## 299        4        2  0.2627964367
## 300        4        2  0.1578221177
## 301        2        4  0.1926801492
## 302        2        4  0.1811557651
## 303        2        3  0.3114683602
## 304        3        2  0.2909466681
## 305        3        4  0.2844400776
## 306        2        4 -0.0801811943
## 307        2        1  0.1216265340
## 308        3        2  0.0939715756
## 309        2        3 -0.0620336643
## 310        3        2  0.2465072126
## 311        3        4  0.4041980246
## 312        3        4  0.3131909969
## 313        3        4  0.3997470379
## 314        3        4  0.4045983171
## 315        3        4  0.3375018716
## 316        3        4  0.1464339834
## 317        3        4  0.1340848704
## 318        3        4  0.1389705964
## 319        2        3  0.0497804214
## 320        2        1  0.2505747110
## 321        2        1  0.0531903262
## 322        4        2  0.4495500783
## 323        4        1  0.3492960673
## 324        2        4  0.2916836611
## 325        3        4  0.1669127128
## 326        3        4  0.2002669240
## 327        3        4  0.2846612166
## 328        3        4  0.1439924453
## 329        3        4  0.2681270288
## 330        2        3  0.1326172141
## 331        4        2  0.2373959365
## 332        4        2  0.2063261344
## 333        2        4  0.1304409351
## 334        4        2  0.1596573502
## 335        4        3  0.1775476642
## 336        2        4  0.1878737717
## 337        2        4 -0.0748388356
## 338        4        3  0.3450667217
## 339        4        3  0.2544954720
## 340        4        2  0.2655364710
## 341        4        2  0.1756819669
## 342        4        2  0.3889184878
## 343        4        2  0.2841174489
## 344        4        2  0.2116876417
## 345        1        4  0.1580683853
## 346        1        4  0.2356511628
## 347        1        4  0.1490560829
## 348        1        4  0.3364468389
## 349        1        2  0.1954910643
## 350        1        4  0.3605873026
## 351        1        4  0.3751754392
## 352        1        4  0.3443751894
## 353        1        4  0.3563056349
## 354        1        4  0.3166491490
## 355        1        4  0.1627720302
## 356        1        4 -0.0711113041
## 357        4        1  0.1653143962
## 358        4        1  0.3234474487
## 359        1        4  0.1917533663
## 360        1        4  0.3683707308
## 361        1        4  0.2514863439
## 362        1        4  0.2035368247
## 363        1        4  0.2209201922
## 364        1        4  0.2876320223
## 365        1        4  0.2843499377
## 366        1        4  0.0385099924
## 367        1        4  0.1263178038
## 368        1        4  0.2605338978
## 369        1        4  0.3514134181
## 370        1        4  0.3074401564
## 371        1        4  0.3118427570
## 372        1        4  0.3307348221
## 373        1        4  0.3313016465
## 374        1        4  0.2970200589
## 375        4        1  0.3014989788
## 376        1        4 -0.0548341724
## 377        4        1  0.3202536996
## 378        4        1  0.1924934931
## 379        1        4  0.2694945636
## 380        1        4  0.3079079987
## 381        1        4  0.3519319716
## 382        1        4  0.3554349134
## 383        1        4  0.1839960582
## 384        4        1  0.2051041070
## 385        1        4  0.1639569993
## 386        2        1  0.0696599903
## 387        1        4  0.2033416545
## 388        1        4 -0.0755550476
## 389        4        1  0.2716695318
## 390        1        4 -0.0562473158
## 391        1        4  0.2710750825
## 392        1        4  0.3569719622
## 393        1        4 -0.1029564202
## 394        4        1  0.2105975780
## 395        1        4 -0.0288675923
## 396        4        1  0.2379167849
## 397        4        1  0.3427204407
## 398        4        1  0.1177646996
## 399        1        4 -0.0287056050
## 400        4        1  0.2725548297
## 401        4        1  0.2215291610
## 402        1        4 -0.0188495749
## 403        1        4  0.2163874455
## 404        1        4  0.1632086729
## 405        1        4  0.0340554753
## 406        1        4  0.1094434781
## 407        1        4  0.2700620248
## 408        1        4  0.2270892913
## 409        1        4  0.0702793776
## 410        1        4 -0.0106902508
## 411        1        4 -0.0407764158
## 412        1        4  0.2179195745
## 413        1        4  0.2505724287
## 414        1        4  0.1356243158
## 415        4        1  0.1338928793
## 416        1        4 -0.0784556549
## 417        1        4  0.0251247193
## 418        1        4  0.1319590880
## 419        4        1  0.2452097563
## 420        4        1  0.2951867592
## 421        4        1  0.4054746541
## 422        4        1  0.4497430696
## 423        4        1  0.2699372623
## 424        1        4  0.0638144435
## 425        1        4  0.1951551553
## 426        1        4  0.1185727735
## 427        1        4  0.1864830081
## 428        1        4  0.2751619786
## 429        1        2 -0.0260103934
## 430        4        3  0.3500926213
## 431        4        2  0.3931574742
## 432        4        1  0.2688709720
## 433        4        1  0.4273602003
## 434        4        1  0.4568334456
## 435        4        1  0.4242777832
## 436        4        1  0.4149528732
## 437        4        1  0.3321093486
## 438        4        1  0.3273432427
## 439        1        4  0.0639465288
## 440        1        4  0.1112016926
## 441        1        4  0.0687136982
## 442        1        4 -0.1199187528
## 443        1        2  0.1441634888
## 444        1        2  0.0444371051
## 445        1        4  0.3607353283
## 446        1        4  0.2661210354
## 447        1        4  0.3167348328
## 448        1        4  0.3208435144
## 449        1        4  0.3368697968
## 450        1        4  0.0164100933
## 451        4        1  0.2380158328
## 452        4        1  0.4919623956
## 453        1        2  0.0214498719
## 454        1        4  0.0619870489
## 455        4        2  0.3557056618
## 456        2        4  0.0649436723
## 457        2        1  0.1252708501
## 458        2        4  0.2196840000
## 459        2        3  0.1365827147
## 460        2        4 -0.0026918339
## 461        2        4 -0.1057800311
## 462        2        4  0.0719542446
## 463        2        4 -0.0349601315
## 464        4        2  0.2634382542
## 465        4        2  0.1381752626
## 466        2        4  0.1194490230
## 467        4        2  0.1029990826
## 468        3        4  0.3998674304
## 469        3        4  0.3393669085
## 470        2        3 -0.0508956387
## 471        3        4  0.3689124094
## 472        3        4  0.3869453021
## 473        3        4  0.3875454721
## 474        3        4  0.1956789962
## 475        3        4 -0.0172141328
## 476        2        4  0.0853677129
## 477        1        2  0.0971179433
## 478        2        1  0.0927444564
## 479        2        4 -0.0233224364
## 480        3        4  0.3364763085
## 481        3        4  0.3815713652
## 482        3        2  0.2857057785
## 483        2        4  0.2327659307
## 484        2        1  0.0839920284
## 485        1        2  0.0449510726
## 486        2        4 -0.0245917942
## 487        4        2  0.2840139853
## 488        2        3  0.0411873272
## 489        2        3  0.0160248780
## 490        2        3  0.2060184811
## 491        2        3  0.0374383971
## 492        2        4  0.1121109040
## 493        2        4  0.1768797633
## 494        2        4  0.2877904313
## 495        3        2  0.1697431393
## 496        2        3  0.3256606984
## 497        2        1  0.1115259437
## 498        2        4  0.1721314265
## 499        2        1  0.2536159249
## 500        2        1  0.1542300179
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## 1915       3        2  0.5518508556
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## 1920       3        2  0.4249851735
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## 1927       3        2  0.4816670901
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## 1929       2        3 -0.0077555943
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## 1931       2        3  0.1027264226
## 1932       2        3  0.0844285857
## 1933       3        2  0.3957954012
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## 1935       3        2  0.4600195269
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## 1937       3        2  0.4349920104
## 1938       3        2  0.3322358625
## 1939       3        2  0.3104619424
## 1940       2        3  0.1693691421
## 1941       2        3 -0.0713077917
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## 1947       3        2  0.3938671580
## 1948       3        4  0.4370058487
## 1949       3        4  0.2068644383
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## 1953       3        2  0.1545067614
## 1954       3        2  0.1379443849
## 1955       3        2  0.3630954789
## 1956       3        2  0.4300070139
## 1957       3        2  0.4644910871
## 1958       3        2  0.2738198237
## 1959       3        2  0.2454239156
## 1960       3        2  0.3972305031
## 1961       3        2  0.3386993972
## 1962       3        2  0.4004276839
## 1963       3        2  0.4600949260
## 1964       3        2  0.4562193323
## 1965       3        2  0.5134546248
## 1966       3        2  0.5066084744
## 1967       3        2  0.5003061908
## 1968       3        2  0.5052101758
## 1969       3        2  0.5234673076
## 1970       3        2  0.4930218973
## 1971       3        4  0.4786650353
## 1972       3        2  0.3909436948
## 1973       3        2  0.3681997721
## 1974       3        2  0.1525044285
## 1975       2        4 -0.0976831577
## 1976       2        3 -0.0016208732
## 1977       3        2  0.1523287194
## 1978       3        2  0.3237311203
## 1979       2        3  0.2572743779
## 1980       2        3 -0.0558321819
## 1981       3        2  0.3578063906
## 1982       3        2  0.4109990844
## 1983       3        2  0.5458492525
## 1984       3        2  0.2710171677
## 1985       3        2  0.2749761608
## 1986       3        4  0.5006927120
## 1987       3        2  0.3733702824
## 1988       3        2  0.5414714790
## 1989       3        2  0.3404846396
## 1990       3        2  0.5111457766
## 1991       3        2  0.4951908139
## 1992       3        4  0.0689831110
## 1993       2        3  0.0281967825
## 1994       2        3  0.1872626627
## 1995       3        2  0.3382218284
## 1996       3        2  0.3959864891
## 1997       3        2  0.3262376325
## 1998       2        3  0.0990237861
## 1999       2        3  0.2231346767
## 2000       2        3  0.1606632726
## 2001       3        2  0.1845172435
## 2002       3        2  0.4137367906
## 2003       3        2  0.3324402327
## 2004       3        2  0.2246284457
## 2005       3        2  0.2077348010
## 2006       3        4  0.3149665217
## 2007       3        4  0.4790121561
## 2008       3        4  0.4723239722
## 2009       3        2  0.4684801756
## 2010       3        4  0.0993691292
## 2011       3        4  0.3959330522
## 2012       3        4  0.2181693555
## 2013       3        4  0.4298365974
## 2014       3        2  0.5161741526
## 2015       3        4  0.5139318440
## 2016       3        2  0.4868460430
## 2017       3        4  0.4896611994
## 2018       3        4  0.3949327921
## 2019       3        2  0.0991364021
## 2020       3        2  0.1908577580
## 2021       3        4  0.2199202214
## 2022       3        4  0.1699623113
## 2023       3        4  0.3607956594
## 2024       3        4  0.2379137702
## 2025       3        4  0.4309486715
## 2026       3        4  0.3349626485
## 2027       2        4  0.2566825457
## 2028       1        4 -0.0252678627
## 2029       2        3 -0.0401763617
## 2030       3        4  0.4816455134
## 2031       3        4  0.4753432642
## 2032       3        4  0.2252024983
## 2033       2        3 -0.0202047516
## 2034       3        4  0.3709944630
## 2035       3        4  0.4418517663
## 2036       3        2  0.3517183030
## 2037       3        4  0.2379763486
## 2038       2        3  0.2011591134
## 2039       3        2  0.3576672618
## 2040       3        4  0.3441383381
## 2041       3        4  0.0458769189
## 2042       4        3  0.3405136335
## 2043       4        2  0.2426041296
## 2044       2        4  0.2546495199
## 2045       2        3 -0.0694574266
## 2046       3        4  0.1947477799
## 2047       4        2  0.3022853798
## 2048       1        2  0.0700473532
## 2049       1        4  0.2831902056
## 2050       2        4  0.3286809582
## 2051       3        4  0.3148646830
## 2052       3        4  0.0495080480
## 2053       3        4  0.0547127280
## 2054       4        3  0.2635314881
## 2055       4        1  0.2896018028
## 2056       4        1  0.4707994413
## 2057       4        1  0.2807636529
## 2058       4        1  0.4821265116
## 2059       4        1  0.3930068193
## 2060       1        4  0.1409011029
## 2061       1        4  0.0695237685
## 2062       4        1  0.1296185686
## 2063       4        1  0.2562705466
## 2064       4        1  0.3937455333
## 2065       4        1  0.4904799153
## 2066       4        1  0.4835368738
## 2067       4        1  0.4663607827
## 2068       4        1  0.4750143695
## 2069       4        1  0.4523500284
## 2070       4        1  0.4146678952
## 2071       4        1  0.5324766519
## 2072       4        3  0.3164165647
## 2073       4        3  0.3172826770
## 2074       4        3  0.4891984932
## 2075       4        1  0.2486217741
## 2076       1        4  0.0462896689
## 2077       1        4  0.0722366752
## 2078       2        4  0.2643155923
## 2079       4        2  0.1958405161
## 2080       4        2  0.3616649336
## 2081       4        2  0.3566159972
## 2082       4        3  0.3763173845
## 2083       4        3  0.4985502404
## 2084       4        3  0.4734306775
## 2085       4        1  0.5116522263
## 2086       4        1  0.4798094518
## 2087       4        1  0.4504659338
## 2088       4        1  0.4837159702
## 2089       4        1  0.4568349784
## 2090       4        1  0.3438257434
## 2091       1        4 -0.0426710469
## 2092       1        4 -0.0675933922
## 2093       2        1  0.1735846279
## 2094       1        2  0.0116418706
## 2095       1        2  0.2066023623
## 2096       1        4  0.1593777920
## 2097       1        4  0.1697806378
## 2098       1        4  0.2096865516
## 2099       1        4 -0.1037784444
## 2100       1        4  0.3305906133
## 2101       1        4  0.3694349642
## 2102       1        4  0.2421846000
## 2103       1        4  0.0688112925
## 2104       1        2  0.0999794971
## 2105       1        2  0.1655638481
## 2106       1        4  0.0098904266
## 2107       4        1  0.4450144261
## 2108       4        1  0.3890635987
## 2109       4        1  0.3428493213
## 2110       1        4  0.0209479845
## 2111       4        1  0.4323348517
## 2112       4        1  0.4125108682
## 2113       4        1  0.3602984704
## 2114       1        4  0.2664686106
## 2115       1        4  0.1869383162
## 2116       1        4  0.0580288956
## 2117       1        4  0.3405713184
## 2118       1        4  0.1961613974
## 2119       1        4  0.2856005627
## 2120       1        4  0.2151604732
## 2121       1        4  0.0413346323
## 2122       1        4  0.1062223607
## 2123       1        4  0.0846663422
## 2124       1        4  0.1900993759
## 2125       1        4  0.2167852451
## 2126       1        4  0.3079669921
## 2127       1        4  0.2589073479
## 2128       1        2  0.1414107063
## 2129       1        4  0.2760382761
## 2130       1        4  0.2951093321
## 2131       1        4  0.2778994350
## 2132       1        4  0.3032107360
## 2133       1        4  0.3035240517
## 2134       1        4  0.3693992774
## 2135       1        4  0.3493379557
## 2136       1        4  0.3437682710
## 2137       1        4  0.3725390347
## 2138       1        4  0.3680210258
## 2139       1        4  0.2653587801
## 2140       1        4  0.3616124656
## 2141       1        4  0.3373857905
## 2142       1        4  0.3961371280
## 2143       1        4  0.3424471421
## 2144       1        4  0.2329120627
## 2145       1        4 -0.0338910197
## 2146       1        4  0.0371488096
## 2147       1        4 -0.0835569560
## 2148       1        4  0.1724552263
## 2149       1        4  0.2866113872
## 2150       1        4  0.3352170340
## 2151       1        4  0.3012083638
## 2152       1        4  0.2158680726
## 2153       1        4  0.2576792103
## 2154       1        4  0.2646317137
## 2155       4        1  0.1705421455
## 2156       4        1  0.3976763751
## 2157       4        1  0.1809871710
## 2158       4        1  0.2001328817
## 2159       1        4  0.0347091012
## 2160       1        4 -0.0374740357
## 2161       1        4  0.0136020926
## 2162       4        1  0.1691842782
## 2163       4        1  0.1673968734
## 2164       1        4  0.0562546046
## 2165       4        1  0.2169891632
## 2166       4        1  0.0948940834
## 2167       1        4  0.0802352380
## 2168       1        4  0.1661175164
## 2169       1        4  0.1099178031
## 2170       1        4  0.1038198709
## 2171       1        4  0.3104563006
## 2172       1        4  0.1667470616
## 2173       1        2  0.0424152866
## 2174       1        4  0.3445393509
## 2175       4        1  0.1495009897
## 2176       4        1  0.2843645829
## 2177       4        1  0.3499904091
## 2178       4        1  0.2975215366
## 2179       4        1  0.3500133238
## 2180       1        4 -0.0614138036
## 2181       1        4  0.2403268870
## 2182       1        4  0.2604033323
## 2183       1        4  0.1613585782
## 2184       1        4  0.2126385231
## 2185       1        4  0.0157110557
## 2186       1        4  0.1649323221
## 2187       4        1  0.4787749245
## 2188       4        3  0.5376096730
## 2189       4        1  0.3565478097
## 2190       4        1  0.5087858023
## 2191       4        1  0.4862494789
## 2192       4        1  0.3743409654
## 2193       4        1  0.2494576863
## 2194       1        4 -0.0337380201
## 2195       4        1  0.1704747770
## 2196       4        1  0.1592553592
## 2197       4        1  0.2106864750
## 2198       1        4  0.0853727421
## 2199       1        4 -0.0360255786
## 2200       4        1  0.3301707538
## 2201       4        1  0.4125816313
## 2202       4        1  0.1258965432
## 2203       4        1  0.3576402606
## 2204       4        1  0.4761499764
## 2205       4        1  0.2098624376
## 2206       1        4  0.3423333299
## 2207       1        4 -0.1415244706
## 2208       4        2  0.4323998771
## 2209       4        3  0.3740367447
## 2210       4        3  0.3098632896
## 2211       4        1  0.1898573904
## 2212       4        1  0.2678504333
## 2213       4        3  0.4885925578
## 2214       4        1  0.4826346708
## 2215       1        4  0.1220608446
## 2216       1        4 -0.0632731702
## 2217       1        4 -0.0658347537
## 2218       2        1  0.1043585929
## 2219       1        2  0.0163431568
## 2220       1        4  0.2224613406
## 2221       1        2  0.1085729669
## 2222       1        4  0.1093414110
## 2223       2        1  0.1046820074
## 2224       4        3  0.3381855886
## 2225       4        3  0.2550150586
## 2226       4        2  0.3763321085
## 2227       4        2  0.2424553045
## 2228       4        3  0.3494919180
## 2229       4        3  0.2429482954
## 2230       4        2  0.2423585568
## 2231       4        2  0.1647701615
## 2232       4        3  0.3614788345
## 2233       2        3  0.1977634209
## 2234       4        3  0.1010305712
## 2235       2        4 -0.0303960142
## 2236       2        4 -0.0774102270
## 2237       2        4  0.2461130640
## 2238       4        2  0.1375276673
## 2239       1        2  0.0266749464
## 2240       4        1  0.3375503093
## 2241       4        3  0.2508093661
## 2242       3        2  0.3127938671
## 2243       2        3 -0.0693181283
## 2244       3        4  0.5187868081
## 2245       3        4  0.4327863561
## 2246       3        4  0.3714631380
## 2247       2        3 -0.0044011192
## 2248       2        1  0.2504712817
## 2249       2        1  0.0638847246
## 2250       2        4  0.2495208523
## 2251       2        4  0.1891500923
## 2252       2        4  0.1470620722
## 2253       2        4 -0.0580411825
## 2254       3        4  0.2795152808
## 2255       3        4  0.4480745079
## 2256       3        2  0.4590713825
## 2257       3        4  0.4817258429
## 2258       3        2  0.5345956046
## 2259       3        4  0.5066516813
## 2260       3        4  0.4382915414
## 2261       3        2  0.2743020564
## 2262       3        2  0.1179894422
## 2263       2        4  0.1774739792
## 2264       2        1  0.1194462894
## 2265       2        4  0.3126640334
## 2266       2        4  0.3352881776
## 2267       2        4  0.1772610226
## 2268       2        3 -0.0275646394
## 2269       3        2  0.2301467001
## 2270       2        4  0.1479540006
## 2271       2        3  0.2517153758
## 2272       3        2  0.3705807180
## 2273       3        2  0.4921025981
## 2274       3        2  0.3362116945
## 2275       3        4  0.3613471632
## 2276       3        2  0.3402095519
## 2277       3        2  0.5103865268
## 2278       2        3  0.2096379566
## 2279       2        1  0.2529239014
## 2280       2        4  0.1831046909
## 2281       2        3  0.3264757453
## 2282       2        3  0.3536655871
## 2283       3        2  0.3503004410
## 2284       3        2  0.4873025056
## 2285       3        2  0.3789216668
## 2286       3        2  0.4700581547
## 2287       3        4  0.5122766809
## 2288       3        2  0.4549885266
## 2289       3        2  0.3003511329
## 2290       3        2  0.5383088055
## 2291       3        2  0.5516206277
## 2292       2        3  0.1023778293
## 2293       3        2  0.3686906695
## 2294       2        4  0.2824393479
## 2295       2        4  0.1655664910
## 2296       2        4  0.2912438482
## 2297       2        3  0.2600002971
## 2298       2        4  0.0080791215
## 2299       2        3  0.0654694756
## 2300       2        3  0.1599058407
## attr(,"Ordered")
## [1] FALSE
## attr(,"call")
## silhouette.default(x = kmeans.result$cluster, dist = dist(data.cr))
## attr(,"class")
## [1] "silhouette"

Cluster 2 a des silhouettes proches de 1, donc bien placés. Cluster 1 a des individus dont les silhouettes sont négatives, donc mal placés.

PAM

pam.result <- pam(data.cr, K)
pam.result
## Medoids:
##        ID    MinTemp    MaxTemp   Rainfall Humidity9am Humidity3pm Pressure9am
## [1,] 1465  0.1682661  0.4643129 -0.3243074  -0.4104022  -0.4142087   0.2924229
## [2,] 1800  1.0711497  1.2798301 -0.3243074   0.4060714   0.5087682  -0.6204501
## [3,]  554 -0.5901561 -0.5365490  0.5004635   0.7326608   0.6765822  -0.9247412
## [4,]  625 -0.9151943 -0.8701697 -0.3046700  -0.9002864  -0.6659297   0.8473065
##      Pressure3pm    Temp9am    Temp3pm    AvgTemp
## [1,]   0.2142630  0.2695290  0.2564509  0.3245658
## [2,]  -0.4872648  1.2873306  1.0781070  1.2122462
## [3,]  -1.0041800 -0.5220945 -0.4905092 -0.5820013
## [4,]   1.0265583 -1.0121472 -0.7892933 -0.9219640
## Clustering vector:
##    [1] 1 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2
##   [38] 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1
##   [75] 1 1 1 1 1 1 2 2 2 1 1 1 1 1 2 1 2 2 2 2 1 1 1 1 3 2 2 2 2 1 1 1 1 1 1 1 1
##  [112] 1 1 1 2 1 1 1 1 1 1 4 1 1 1 3 3 3 3 3 3 3 3 3 3 3 1 3 3 1 1 3 3 3 3 3 3 4
##  [149] 3 3 2 1 1 1 3 3 3 3 4 3 4 4 4 4 4 4 4 3 3 4 4 3 4 4 4 4 4 3 4 4 4 4 4 3 3
##  [186] 4 4 3 4 4 4 4 4 4 4 3 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 1 1 3 3 4 4 3 4 4 4 4
##  [223] 4 3 3 4 3 3 4 4 4 3 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 1 1 3 4 4 3 3 4 4 3 3 3
##  [260] 4 4 3 3 4 4 4 4 4 3 3 3 2 4 4 4 4 4 4 4 1 1 1 4 4 4 4 3 3 3 4 4 4 4 4 4 1
##  [297] 1 1 1 1 3 3 3 4 4 1 3 4 3 4 4 4 4 4 4 4 1 1 1 3 3 1 1 3 1 4 4 4 4 1 1 1 3
##  [334] 1 1 3 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
##  [371] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
##  [408] 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 3 1 1 2 2 1 1 1 1 2 2 2 2 2 2 3
##  [445] 2 2 2 2 2 2 2 1 3 2 1 3 3 3 3 1 1 3 3 1 1 3 1 4 4 4 4 4 4 4 1 3 3 3 3 4 4
##  [482] 4 3 3 3 3 1 1 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 4 3 3 4 4 4 4 4 4 4 4 4 3 3 3
##  [519] 3 3 4 4 3 3 4 4 4 4 4 4 4 3 3 3 3 3 3 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 3 3 3
##  [556] 3 3 4 4 4 3 4 4 4 3 4 4 4 3 3 4 4 3 4 4 4 4 4 4 4 4 4 3 4 3 3 3 4 4 4 4 4
##  [593] 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 4 4 4 3 3 3 3 4 4 4 1 3 4 4 4 4 4 4 4
##  [630] 4 4 1 1 3 3 3 3 3 3 3 4 4 4 4 1 1 1 3 1 4 4 4 1 1 1 1 1 1 1 2 1 1 1 1 1 1
##  [667] 2 2 2 2 2 3 1 1 2 3 2 2 2 2 2 1 1 1 1 1 1 2 1 1 2 3 3 2 2 2 2 2 3 1 1 2 2
##  [704] 2 1 1 1 2 2 1 1 1 2 2 2 2 2 2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2 3 3 2 2 2 2 2
##  [741] 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 1 1 2 2 1 2 2 2 2 1 1 2 2 2 2 2 3
##  [778] 1 2 2 2 1 1 1 1 3 2 2 2 3 2 2 2 3 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2
##  [815] 1 1 1 2 3 4 4 4 1 1 3 1 1 1 1 1 1 3 4 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4
##  [852] 4 3 3 3 3 4 4 4 3 3 3 3 4 4 4 1 4 3 4 4 4 3 4 4 4 4 3 3 3 3 4 4 3 4 4 4 4
##  [889] 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 4 4 3 3 4 3 4 3 4 3 4 4 4 4 4 3 3 3 4 4 4
##  [926] 4 4 4 3 4 4 4 4 4 4 4 3 3 4 3 4 4 3 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4
##  [963] 3 3 3 3 3 4 3 4 4 3 4 4 4 4 4 1 3 3 3 4 3 1 4 4 4 4 4 4 4 1 3 3 3 3 3 4 3
## [1000] 4 3 4 4 3 3 4 4 4 4 4 4 4 4 3 4 4 1 1 1 2 3 3 2 3 3 1 4 1 1 1 1 1 2 2 2 2
## [1037] 1 1 2 1 1 2 2 1 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 1 1 2 1 1 1
## [1074] 2 2 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 1 2 2 2 1 2 2 2 1 1 1 1 1 1 3 1 1 3 3 2
## [1111] 1 1 2 2 2 1 1 1 2 1 1 1 1 1 1 1 3 1 3 1 4 4 4 1 4 4 3 3 3 3 3 3 3 3 3 3 3
## [1148] 3 3 3 4 4 4 4 4 4 1 3 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 4 4 4 4 4 3 3 4 4
## [1185] 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 3 3 3 3 4 4
## [1222] 4 4 3 3 3 3 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3
## [1259] 3 3 4 4 3 3 4 3 3 3 3 3 3 3 3 1 3 3 4 4 4 4 1 3 3 3 3 4 4 1 1 4 1 3 4 4 4
## [1296] 4 4 4 4 4 1 1 3 3 4 4 1 3 1 4 4 4 3 1 3 1 4 4 4 1 1 1 1 1 2 2 3 3 3 3 3 3
## [1333] 2 2 2 3 1 2 2 3 1 2 2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1
## [1370] 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 2 2 3 2 2 2 2 2 2 1 1 1 1 1 2 2 2 3 3 2
## [1407] 2 1 1 1 2 1 1 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 2 3 2 2
## [1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3 3 1 1 2 2 2 2 2 2 2 1 1 1
## [1481] 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 4 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 1 4 4
## [1518] 3 3 4 4 4 4 4 3 3 3 3 3 3 3 3 3 4 3 3 3 3 4 4 4 4 4 3 3 1 4 4 4 3 3 4 4 4
## [1555] 4 3 3 3 3 4 3 3 3 3 4 4 4 3 3 3 3 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4
## [1592] 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 3 3 3 4 4 4 4
## [1629] 3 3 3 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 1 1 3 4 4 4 4 4 1 3 3 4 4 4 4 4
## [1666] 4 4 4 4 1 1 1 1 1 2 2 3 4 4 1 1 4 1 4 1 1 4 4 1 2 1 1 1 1 1 1 1 1 1 2 1 1
## [1703] 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 2 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1740] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2
## [1777] 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 1 1 1 1
## [1814] 2 1 1 1 1 1 1 2 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 2 2 2 2
## [1851] 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 3 1 4 4 4 4 4 4 1 3 4 4 4 4 4 4 4 1 3 1 3
## [1888] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 3 3 4 4
## [1925] 4 4 4 3 3 4 3 3 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4
## [1962] 4 4 4 4 4 4 4 4 4 4 4 4 4 1 3 1 4 3 3 4 4 4 4 4 4 4 4 4 4 4 1 1 3 4 4 4 3
## [1999] 3 3 4 4 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 4 4 4 4 3 4 4
## [2036] 4 4 3 4 4 1 1 1 3 1 4 1 2 2 3 4 1 1 1 2 1 2 1 2 2 2 2 2 2 1 1 1 1 1 2 1 1
## [2073] 1 1 2 2 2 3 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
## [2110] 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2147] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2
## [2184] 2 2 2 1 1 2 1 1 2 2 2 2 2 2 2 2 1 1 2 1 1 2 2 2 1 1 1 1 1 1 1 2 2 2 3 3 2
## [2221] 2 2 3 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 3 1 1 4 4 4 4 4 1 3 3 3 3 3 1 4 4 4 4
## [2258] 4 4 4 4 1 3 3 3 3 3 3 4 3 3 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 3 4 3
## [2295] 3 3 3 1 3 3
## Objective function:
##    build     swap 
## 1.944706 1.910137 
## 
## Available components:
##  [1] "medoids"    "id.med"     "clustering" "objective"  "isolation" 
##  [6] "clusinfo"   "silinfo"    "diss"       "call"       "data"
par(mfrow=c(1,2))
plot(pam.result)

# le premier graphe correspond à l'ACP.
# le deuxième graphe aux silhouettes.
table(pam.result$clustering, kmeans.result$cluster)
##    
##       1   2   3   4
##   1   0  53  40 426
##   2 388   0   0 214
##   3  43 400   7   1
##   4   0  15 713   0
res=FAMD(dataReady)
## Warning: ggrepel: 2276 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

## Warning: ggrepel: 2276 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

On lance CAH avec la fonction HCPC

cah = HCPC(res, nb.clust = 4)